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## Equation Word Problems Worksheets

This compilation of a meticulously drafted equation word problems worksheets is designed to get students to write and solve a variety of one-step, two-step and multi-step equations that involve integers, fractions, and decimals. These worksheets are best suited for students in grade 6 through high school. Click on the 'Free' icons to sample our handouts.

One Step Equation Word Problem Worksheets

Read and solve this series of word problems that involve one-step equations. Apply basic operations to find the value of unknowns.

(15 Worksheets)

Two-Step Equation Word Problems: Integers

Interpret this set of word problems that require two-step operations to solve the equations. Each printable worksheet has five word problems ideal for 6th grade, 7th grade, and 8th grade students.

Two-Step Equation Word Problems: Fractions and Decimals

Read each word problem and set up the two-step equation. Solve the equation and find the solution. This selection of worksheets includes both fractions and decimals.

MCQ - Two-Step Equation Word Problems

Pick the correct two-step equation that best matches word problems presented here. Evaluate the ability of students to solve two-step equations with this array of MCQ worksheets.

Multi-Step Equation Word Problems: Integers

Read each multi-step word problem in these high school pdf worksheets and set up the equation. Solve and find the value of the unknown. More than two steps are required to solve the problems.

Multi-step equation Word Problems: Fractions and Decimals

Write multi-step equations that involve both fractions and decimals based on the word problems provided here. Validate your responses with our answer keys.

Related Worksheets

» One-step Equation

» Two-step Equation

» Multi-step Equation

» Algebraic Identities

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## Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

## Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

## Turning English into Algebra

To turn the English into Algebra it helps to:

- Read the whole thing first
- Do a sketch if possible
- Assign letters for the values
- Find or work out formulas

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

## Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

## Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

- Let S = dollars Sam has
- Let A = dollars Alex has

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

## Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

- Let D = number of dogs
- Let C = number of cats

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

## Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

- Use w for width of rectangle: w = 12m
- Use h for height of rectangle: h = 5m

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

## Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

- Use S for how many games Sam played
- Use A for how many games Alex played

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

## Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

- Use a for Alex's work rate
- Use s for Sam's work rate

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

## Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

- The number of "5 hour" days: d
- The number of "3 hour" days: e

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

## Example: A circle has an area of 12 mm 2 , what is its radius?

- Use A for Area: A = 12 mm 2
- Use r for radius

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

## Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

- Use V for Volume
- Use A for Area
- Use s for side length of cube
- Volume of a cube: V = s 3
- Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

## Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

- Joel's normal rate of pay: $N per hour
- Joel works for 40 hours at $N per hour = $40N
- When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
- Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
- And together he earned $660, so:

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

## Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

- Present Value PV = $2,000
- Interest Rate (as a decimal): r = 0.11
- Number of Periods: n = 3
- Future Value (the value we want): FV

We are being asked for the Future Value: FV

## Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

- Present Value PV = $1,000
- Interest Rate (the value we want): r
- Number of Periods: n = 9
- Future Value: FV = $1,551.33

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

## Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

- Number of boys now: b
- Number of girls now: g

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

## Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

n(n + 2) = 168

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

- We could try, say, n=10: 10(12) = 120 NO (too small)
- Next we could try n=12: 12(14) = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

## Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

- the length of the room: L
- the width of the room: W
- the total Area including veranda: A
- the width of the room is half its length: W = ½L
- the total area is the (room width + 3) times the length: A = (W+3) × L = 56

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

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## Algebra Topics - Introduction to Word Problems

Algebra topics -, introduction to word problems, algebra topics introduction to word problems.

## Algebra Topics: Introduction to Word Problems

Lesson 9: introduction to word problems.

/en/algebra-topics/solving-equations/content/

## What are word problems?

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem. For instance, does this sound familiar?

Johnny has 12 apples. If he gives four to Susie, how many will he have left?

You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you're supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with 12 apples. By the end, he has 4 less because he gave them away. You could write this as:

12 - 4 = 8 , so you know Johnny has 8 apples left.

## Word problems in algebra

If you were able to solve this problem, you should also be able to solve algebra word problems. Yes, they involve more complicated math, but they use the same basic problem-solving skills as simpler word problems.

You can tackle any word problem by following these five steps:

- Read through the problem carefully, and figure out what it's about.
- Represent unknown numbers with variables.
- Translate the rest of the problem into a mathematical expression.
- Solve the problem.
- Check your work.

We'll work through an algebra word problem using these steps. Here's a typical problem:

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost $360. How many miles did she drive?

It might seem complicated at first glance, but we already have all of the information we need to solve it. Let's go through it step by step.

## Step 1: Read through the problem carefully.

With any problem, start by reading through the problem. As you're reading, consider:

- What question is the problem asking?
- What information do you already have?

Let's take a look at our problem again. What question is the problem asking? In other words, what are you trying to find out?

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. How many miles did she drive?

There's only one question here. We're trying to find out how many miles Jada drove . Now we need to locate any information that will help us answer this question.

There are a few important things we know that will help us figure out the total mileage Jada drove:

- The van cost $30 per day.
- In addition to paying a daily charge, Jada paid $0.50 per mile.
- Jada had the van for 2 days.
- The total cost was $360 .

## Step 2: Represent unknown numbers with variables.

In algebra, you represent unknown numbers with letters called variables . (To learn more about variables, see our lesson on reading algebraic expressions .) You can use a variable in the place of any amount you don't know. Looking at our problem, do you see a quantity we should represent with a variable? It's often the number we're trying to find out.

Since we're trying to find the total number of miles Jada drove, we'll represent that amount with a variable—at least until we know it. We'll use the variable m for miles . Of course, we could use any variable, but m should be easy to remember.

## Step 3: Translate the rest of the problem.

Let's take another look at the problem, with the facts we'll use to solve it highlighted.

The rate to rent a small moving van is $30 per day , plus $0.50 per mile . Jada rented a van to drive to her new home. It took 2 days , and the van cost $360 . How many miles did she drive?

We know the total cost of the van, and we know that it includes a fee for the number of days, plus another fee for the number of miles. It's $30 per day, and $0.50 per mile. A simpler way to say this would be:

$30 per day plus $0.50 per mile is $360.

If you look at this sentence and the original problem, you can see that they basically say the same thing: It cost Jada $30 per day and $0.50 per mile, and her total cost was $360 . The shorter version will be easier to translate into a mathematical expression.

Let's start by translating $30 per day . To calculate the cost of something that costs a certain amount per day, you'd multiply the per-day cost by the number of days—in other words, 30 per day could be written as 30 ⋅ days, or 30 times the number of days . (Not sure why you'd translate it this way? Check out our lesson on writing algebraic expressions .)

$30 per day and $.50 per mile is $360

$30 ⋅ day + $.50 ⋅ mile = $360

As you can see, there were a few other words we could translate into operators, so and $.50 became + $.50 , $.50 per mile became $.50 ⋅ mile , and is became = .

Next, we'll add in the numbers and variables we already know. We already know the number of days Jada drove, 2 , so we can replace that. We've also already said we'll use m to represent the number of miles, so we can replace that too. We should also take the dollar signs off of the money amounts to make them consistent with the other numbers.

30 ⋅ 2 + .5 ⋅ m = 360

Now we have our expression. All that's left to do is solve it.

## Step 4: Solve the problem.

This problem will take a few steps to solve. (If you're not sure how to do the math in this section, you might want to review our lesson on simplifying expressions .) First, let's simplify the expression as much as possible. We can multiply 30 and 2, so let's go ahead and do that. We can also write .5 ⋅ m as 0.5 m .

60 + .5m = 360

Next, we need to do what we can to get the m alone on the left side of the equals sign. Once we do that, we'll know what m is equal to—in other words, it will let us know the number of miles in our word problem.

We can start by getting rid of the 60 on the left side by subtracting it from both sides .

The only thing left to get rid of is .5 . Since it's being multiplied with m , we'll do the reverse and divide both sides of the equation with it.

.5 m / .5 is m and 300 / 0.50 is 600 , so m = 600 . In other words, the answer to our problem is 600 —we now know Jada drove 600 miles.

## Step 5: Check the problem.

To make sure we solved the problem correctly, we should check our work. To do this, we can use the answer we just got— 600 —and calculate backward to find another of the quantities in our problem. In other words, if our answer for Jada's distance is correct, we should be able to use it to work backward and find another value, like the total cost. Let's take another look at the problem.

According to the problem, the van costs $30 per day and $0.50 per mile. If Jada really did drive 600 miles in 2 days, she could calculate the cost like this:

$30 per day and $0.50 per mile

30 ⋅ day + .5 ⋅ mile

30 ⋅ 2 + .5 ⋅ 600

According to our math, the van would cost $360, which is exactly what the problem says. This means our solution was correct. We're done!

While some word problems will be more complicated than others, you can use these basic steps to approach any word problem. On the next page, you can try it for yourself.

Let's practice with a couple more problems. You can solve these problems the same way we solved the first one—just follow the problem-solving steps we covered earlier. For your reference, these steps are:

If you get stuck, you might want to review the problem on page 1. You can also take a look at our lesson on writing algebraic expressions for some tips on translating written words into math.

Try completing this problem on your own. When you're done, move on to the next page to check your answer and see an explanation of the steps.

A single ticket to the fair costs $8. A family pass costs $25 more than half of that. How much does a family pass cost?

Here's another problem to do on your own. As with the last problem, you can find the answer and explanation to this one on the next page.

Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo. Between the two of them, they donated $280. How much money did Mo give?

## Problem 1 Answer

Here's Problem 1:

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

Answer: $29

Let's solve this problem step by step. We'll solve it the same way we solved the problem on page 1.

## Step 1: Read through the problem carefully

The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it . Let's look at the problem again. The question is right there in plain sight:

So is the information we'll need to answer the question:

- A single ticket costs $8 .
- The family pass costs $25 more than half the price of the single ticket.

## Step 2: Represent the unknown numbers with variables

The unknown number in this problem is the cost of the family pass . We'll represent it with the variable f .

## Step 3: Translate the rest of the problem

Let's look at the problem again. This time, the important facts are highlighted.

A single ticket to the fair costs $8 . A family pass costs $25 more than half that . How much does a family pass cost?

In other words, we could say that the cost of a family pass equals half of $8, plus $25 . To turn this into a problem we can solve, we'll have to translate it into math. Here's how:

- First, replace the cost of a family pass with our variable f .

f equals half of $8 plus $25

- Next, take out the dollar signs and replace words like plus and equals with operators.

f = half of 8 + 25

- Finally, translate the rest of the problem. Half of can be written as 1/2 times , or 1/2 ⋅ :

f = 1/2 ⋅ 8 + 25

## Step 4: Solve the problem

Now all we have to do is solve our problem. Like with any problem, we can solve this one by following the order of operations.

- f is already alone on the left side of the equation, so all we have to do is calculate the right side.
- First, multiply 1/2 by 8 . 1/2 ⋅ 8 is 4 .
- Next, add 4 and 25. 4 + 25 equals 29 .

That's it! f is equal to 29. In other words, the cost of a family pass is $29 .

## Step 5: Check your work

Finally, let's check our work by working backward from our answer. In this case, we should be able to correctly calculate the cost of a single ticket by using the cost we calculated for the family pass. Let's look at the original problem again.

We calculated that a family pass costs $29. Our problem says the pass costs $25 more than half the cost of a single ticket. In other words, half the cost of a single ticket will be $25 less than $29.

- We could translate this into this equation, with s standing for the cost of a single ticket.

1/2s = 29 - 25

- Let's work on the right side first. 29 - 25 is 4 .
- To find the value of s , we have to get it alone on the left side of the equation. This means getting rid of 1/2 . To do this, we'll multiply each side by the inverse of 1/2: 2 .

According to our math, s = 8 . In other words, if the family pass costs $29, the single ticket will cost $8. Looking at our original problem, that's correct!

So now we're sure about the answer to our problem: The cost of a family pass is $29 .

## Problem 2 Answer

Here's Problem 2:

Answer: $70

Let's go through this problem one step at a time.

Start by asking what question the problem is asking you to solve and identifying the information that will help you solve it . What's the question here?

To solve the problem, you'll have to find out how much money Mo gave to charity. All the important information you need is in the problem:

- The amount Flor donated is three times as much the amount Mo donated
- Flor and Mo's donations add up to $280 total

The unknown number we're trying to identify in this problem is Mo's donation . We'll represent it with the variable m .

Here's the problem again. This time, the important facts are highlighted.

Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo . Between the two of them, they donated $280 . How much money did Mo give?

The important facts of the problem could also be expressed this way:

Mo's donation plus Flor's donation equals $280

Because we know that Flor's donation is three times as much as Mo's donation, we could go even further and say:

Mo's donation plus three times Mo's donation equals $280

We can translate this into a math problem in only a few steps. Here's how:

- Because we've already said we'll represent the amount of Mo's donation with the variable m , let's start by replacing Mo's donation with m .

m plus three times m equals $280

- Next, we can put in mathematical operators in place of certain words. We'll also take out the dollar sign.

m + three times m = 280

- Finally, let's write three times mathematically. Three times m can also be written as 3 ⋅ m , or just 3 m .

m + 3m = 280

It will only take a few steps to solve this problem.

- To get the correct answer, we'll have to get m alone on one side of the equation.
- To start, let's add m and 3 m . That's 4 m .
- We can get rid of the 4 next to the m by dividing both sides by 4. 4 m / 4 is m , and 280 / 4 is 70 .

We've got our answer: m = 70 . In other words, Mo donated $70 .

The answer to our problem is $70 , but we should check just to be sure. Let's look at our problem again.

If our answer is correct, $70 and three times $70 should add up to $280 .

- We can write our new equation like this:

70 + 3 ⋅ 70 = 280

- The order of operations calls for us to multiply first. 3 ⋅ 70 is 210.

70 + 210 = 280

- The last step is to add 70 and 210. 70 plus 210 equals 280 .

280 is the combined cost of the tickets in our original problem. Our answer is correct : Mo gave $70 to charity.

/en/algebra-topics/distance-word-problems/content/

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I wrote ____ in the place of total marbles since that is what the problem is asking for (the unknown).

All of this may look oversimplified, but helping children to see the underlying relationship between the quantities is important. Consider now this problem:

Example: Jenny and Kenny together have 37 marbles, and Kenny has 15. How many does Jenny have? Many teachers might try to explain this as a subtraction problem, but in the most fundamental level it is about addition! It still talks about two people having certain amount of marbles together . The relationship between the quantities is the SAME as above, so we still need to write an addition equation. Relationship: Jenny's marbles + Kenny's marbles = Total marbles Equation: _____ + 15 = 37 Then, we can solve the equation ____ + 15 = 37 by subtracting. Using this kind of approach in the elementary grades will help children to set up equations in algebra story problems later.

Example : Jenny, Kenny, and Penny together have 51 marbles. Kenny has double as many marbles as Jenny has, and Penny has 12. How many does Jenny have? The relationship between the quantities is the same, so it is solved the same way: by writing an addition equation. However, we need to denote the number of Jenny's and Kenny's marbles with something. Jenny's marbles are unknown, so we can denote that with the variable n . Then Kenny has 2 n marbles. Relationship: Jenny's marbles + Kenny's marbles + Penny's marbles = Total marbles Equation: n + 2 n + 12 = 51

Example: Jane is on page 79 of her book. The book has 254 pages. How many pages does she still have to read? This time the word " still " clues us in to an additive relationship where one of the addends is missing. You can initially write an empty line for what is not known, and later replace that with a variable. pages already read + pages still to read = pages total + = This equation is of course is then solved by subtraction, but it is better if you view it as an addition situation and write an addition equation for it.

Example: The number of hours that were left in the day was one-third of the number of hours already passed. How many hours were left in the day? (From Grade 5 word problems for kids ) Can you see the general principle governing this problem? It talks about the hours of the day where some hours already passed and some hours left. This, of course, points to addition once again: we have one part of the day, another part, and a total. The only quantity we know is the total hours for the day. We don't know the hours already passed nor the hours left, so initially you can use two empty lines in the equation that shows the basic relationship between the quantities: hours already passed + hours left = total hours = Then, the information in the first sentence gives us another relationship: "The number of hours that were left in the day was one-third of the number of hours already passed." We don't know the amount of hours passed nor the hours left. So let's use the variable p for the hours passed. Then we can write an expression involving p for the hours left, because "hours left is one-third of the hours passed," or hours left = 1/3 p Then writing 1/3 p for the "hours left" in the first equation will give us: hours already passed + hours left = total hours p + 1/3 p = 24 This can be solved using basic algebra or by guess & check.

## Subtraction word problems

One situation that indicates subtraction is difference or how many/much more . However, the presence of the word "more" can indicate either an addition or subtraction, so be careful.

Example: Ted read 17 pages today, and Fred read 28. How many more pages did Fred read? The solution is of course 28 − 17 = 11, but it's not enough to simply announce that – children need also to understand that difference is the result of a subtraction and tells the answer to how many more . Relationship: Pages Fred read − pages Ted read = difference Equation: 28 − 17 = __ Example: Greg has 17 more marbles than Jack. Jack has 15. How many does Greg have? Here the word more has a different meaning. This problem is not about the difference. The question asks how many does Greg have – not what is the difference in the amounts of marbles. It simply states Greg has 17 more compared to Jack, so here the word more simply indicates addition: Greg has as many as Jack AND 17 more, so Greg has 15 + 17 marbles.

Example: The mass of the Great Pyramid is 557t greater than that of the Leaning Tower of Pisa. Stone Henge has a mass of 2695t which is 95t less than the Leaning Tower of Pisa. There once was a Greater Pyramid which had a mass twice that of the Great Pyramid. What was the mass of the Greater Pyramid? (From Grade 5 word problems for kids ) Each of the first three sentences give information that can be translated into an equation. The question is not about how many more so it's not about difference. One thing being greater than another implies you add. One thing being less than another implies you subtract. And one thing being twice something indicates multiplying by 2. When I read this problem, I could immediately see that I could write equations from the different sentences in the problem, but I couldn't see the answer right away. I figured that after writing the equations I would see some way forwad; probably one equation is solved and gives an answer to another equation. The first sentence says, "The mass of the Great Pyramid is 557t greater than that of the Leaning Tower of Pisa". What are the quantities and the relationship between them here? mass of Great Pyramid = mass of the Leaning Tower of Pisa + 557t The second sentence says "Stonehenge has a mass of 2695t which is 95t less than the Leaning Tower of Pisa." Here it gives you a relationship similar to the one above, and it actually spells out the mass of Stonehenge. It's like two separate pieces of information: "Stonehenge weighs 95t less than the tower. Stonehenge weighs 2695t." Less means you subtract. If you have trouble deciding which is subtracted from which, you can think in your mind which is heavier: Stonehenge or the tower? either mass of Stonehenge = mass of tower − 95t or mass of tower = mass of Stonehenge − 95t Now since the mass of Stonehenge is given, you can solve this equation, and from that knowledge you can solve the first equation, and from that go on to the mass of the " Greater Pyramid ".

If the teacher just jumps directly to the number sentences when solving word problems, then the students won't see the step that happens in the mind before that. The quantities and the relationship between them have to be made clear and written down before fiddling with the actual numbers. Finding this relationship should be the most important part of the word problems. One could even omit the actual calculations and concentrate just finding the quantities and relationships.

## Problem of Helen's hair length

Problem. Helen has 2 inches of hair cut off each time she goes to the hair salon. If h equals the length of hair before she cuts it and c equals the length of hair after she cuts it, which equation would you use to find the length of Helen's hair after she visit the hair salon? a. h = 2 − c c. c = h − 2 b. c = 2 − h d. h = c − 2

Solution. Ignoring the letters c and h for now, what are the quantities? What principle or relationship is there between them? Which possibility of the ones listed below is right? Which do you take away from which?

SIMPLE, isn't it?? In the original problem, the equations are given with the help of h and c instead of the long phrases "hair length before cutting" and "hair length after cutting". You can substitute the c , h , and 2 into the relationships above, and then match the equations (1) - (4) with the equations (a) through (d).

## Helping students to write the algebraic equations

One idea that came to mind is to go through the examples above, and more, based on the typical word problems in the math books, and then turn the whole thing around and have students do exercises such as:

money earned − money spent on this - money spent on that = money left

original price − discount percent x original price = discounted price

money earned each month − expenses/taxes each month = money to use each month AND money to use each month × number of months = money to use over a period of time

speed × time = distance AND distance from A to B + distance from B to C = distance from A to C

Why are math word problems SO difficult for elementary school children? Hint: it has to do with a "recipe" that many math lessons follow.

The do's and don'ts of teaching problem solving in math General advice on how you can teach problem solving in elementary, middle, and high school math.

How I Teach Word Problems by Andre Toom (PDF) This article is written by a Russian who immigrated to US and noticed how COLLEGE LEVEL students have difficulties even with the simplest word problems! He describes his ideas on how to fill in the gap formed when students haven't learned how to solve word problems in earlier education.

A list of websites focusing on word problems and problem solving Use these sites to find good word problems to solve. Most are free!

When solving word problems, students must first decide what quantity represents x and then must write all the other quuantities in terms of x. I teach the students to set up arrows according to the language in the problem. All arrows point to x. Example. Harry had 10 less toys than Mark. Sue has twice as many toys as Harry. Set up arrows: Sue--- Harry---Mark Therefore Mark is x, Harry is x-10 and Sue is 2(x-10). Students find this very helpful. Sandy Denny

My idea is the math teacher might teach and understand the students at the same time and everyone would have a sense of humor. So I think she/he will know if the students are listening or not, when after the class, talk to the student and ask what is wrong. Don't hurt the student's feelings. lorence

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Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

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## Equations and Word Problems

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## Equations and Word Problems ( Two Step Equations ) Worksheets

Equations and Word Problems (Two Step Equations) Worksheet 1 – This 10 problem worksheet will help you practice writing and solving two step equations that match real world situations. Equations and Word Problems (Two Step Equations) Worksheet 1 RTF Equations and Word Problems (Two Step Equations) Worksheet 1 PDF Preview Equations and Word Problems Worksheet 1 In Your Web Browser View Answers

Equations and Word Problems (Two Step Equations) Worksheet 2 – This 10 problem worksheet will help you practice writing and solving two step equations that match real world situations. Equations and Word Problems (Two Step Equations) Worksheet 2 RTF Equations and Word Problems (Two Step Equations) Worksheet 2 PDF Preview Equations and Word Problems Worksheet 2 In Your Web Browser View Answers

## Equations and Word Problems ( Combining Like Terms ) Worksheets

Equations and Word Problems (Combining Like Terms) Worksheet 1 – This 10 problem worksheet will help you practice writing and solving equations that match real world situations. You will have to combine like terms and then solve the equation. Equations and Word Problems (Combining Like Terms) Worksheet 1 RTF Equations and Word Problems (Combining Like Terms) Worksheet 1 PDF Preview Equations and Word Problems Worksheet 1 In Your Web Browser View Answers

Equations and Word Problems (Combining Like Terms) Worksheet 2 – This 10 problem worksheet will help you practice writing and solving equations that match real world situations. You will have to combine like terms and then solve the equation. Equations and Word Problems (Combining Like Terms) Worksheet 2 RTF Equations and Word Problems (Combining Like Terms) Worksheet 2 PDF Preview Equations and Word Problem Worksheet 2 In Your Web Browser View Answers

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## Word Problems Linear Equations

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## \(\textbf{1)}\) Joe and Steve are saving money. Joe starts with $105 and saves $5 per week. Steve starts with $5 and saves $15 per week. After how many weeks do they have the same amount of money? Show Equations \(y= 5x+105,\,\,\,y=15x+5\) Show Answer 10 weeks ($155)

\(\textbf{2)}\) mike and sarah collect rocks. together they collected 50 rocks. mike collected 10 more rocks than sarah. how many rocks did each of them collect show equations \(m+s=50,\,\,\,m=s+10\) show answer mike collected 30 rocks, sarah collected 20 rocks., \(\textbf{3)}\) in a classroom the ratio of boys to girls is 2:3. there are 25 students in the class. how many are girls show equations \(b+g=50,\,\,\,3b=2g\) show answer 15 girls (10 boys), \(\textbf{4)}\) kyle makes sandals at home. the sandal making tools cost $100 and he spends $10 on materials for each sandal. he sells each sandal for $30. how many sandals does he have to sell to break even show equations \(c=10x+100,\,\,\,r=30x\) show answer 5 sandals ($150), \(\textbf{5)}\) molly is throwing a beach party. she still needs to buy beach towels and beach balls. towels are $3 each and beachballs are $4 each. she bought 10 items in total and it cost $34. how many beach balls did she get show equations show answer 4 beachballs (6 towels), \(\textbf{6)}\) anna volunteers at a pet shelter. they have cats and dogs. there are 36 pets in total at the shelter, and the ratio of dogs to cats is 4:5. how many cats are at the shelter show equations \(c+d=40,\,\,\,5d=4c\) show answer 20 cats (16 dogs), \(\textbf{7)}\) a store sells oranges and apples. oranges cost $1.00 each and apples cost $2.00 each. in the first sale of the day, 15 fruits were sold in total, and the price was $25. how many of each type of frust was sold show equations \(o+a=15,\,\,\,1o+2a=25\) show answer 10 apples and 5 oranges, \(\textbf{8)}\) the ratio of red marbles to green marbles is 2:7. there are 36 marbles in total. how many are red show equations \(r+g=36,\,\,\,7r=2g\) show answer 8 red marbles (28 green marbles), \(\textbf{9)}\) a tennis club charges $100 to join the club and $10 for every hour using the courts. write an equation to express the cost \(c\) in terms of \(h\) hours playing tennis. show equation the equation is \(c=10h+100\), \(\textbf{10)}\) emma and liam are saving money. emma starts with $80 and saves $10 per week. liam starts with $120 and saves $6 per week. after how many weeks will they have the same amount of money show equations \(e = 10x + 80,\,\,\,l = 6x + 120\) show answer 10 weeks ($180 each), \(\textbf{11)}\) mark and lisa collect stamps. together they collected 200 stamps. mark collected 40 more stamps than lisa. how many stamps did each of them collect show equations \(m + l = 200,\,\,\,m = l + 40\) show answer mark collected 120 stamps, lisa collected 80 stamps., \(\textbf{12)}\) in a classroom, the ratio of boys to girls is 3:5. there are 40 students in the class. how many are boys show equations \(b + g = 40,\,\,\,5b = 3g\) show answer 15 boys (25 girls), \(\textbf{13)}\) lisa is selling handmade jewelry. the materials cost $60, and she sells each piece for $20. how many pieces does she have to sell to break even show equations \(c=60,\,\,\,r=20x\) show answer 3 pieces, \(\textbf{14)}\) tom is buying books and notebooks for school. books cost $15 each, and notebooks cost $3 each. he bought 12 items in total, and it cost $120. how many notebooks did he buy show equations \(b + n = 12,\,\,\,15b+3n=120\) show answer 5 notebooks (7 books), \(\textbf{15)}\) emily volunteers at an animal shelter. they have rabbits and guinea pigs. there are 36 animals in total at the shelter, and the ratio of guinea pigs to rabbits is 4:5. how many guinea pigs are at the shelter show equations \(r + g = 36,\,\,\,5g=4r\) show answer 16 guinea pigs (20 rabbits), \(\textbf{16)}\) mike and sarah are going to a theme park. mike’s ticket costs $40, and sarah’s ticket costs $30. they also bought $20 worth of food. how much did they spend in total show equations \(m + s + f = t,\,\,\,m=40,\,\,\,s=30,\,\,\,f=20\) show answer they spent $90 in total., \(\textbf{17)}\) the ratio of red marbles to blue marbles is 2:3. there are 50 marbles in total. how many are blue show equations \(r + b = 50,\,\,\,3r=2b\) show answer 30 blue marbles (20 red marbles), \(\textbf{18)}\) a pizza restaurant charges $12 for a large pizza and $8 for a small pizza. if a customer buys 5 pizzas in total, and it costs $52, how many large pizzas did they buy show equations \(l + s = 5,\,\,\,12l+8s=52\) show answer they bought 3 large pizzas (2 small pizzas)., \(\textbf{19)}\) the area of a rectangle is 48 square meters. if the length is 8 meters, what is the width of the rectangle show equations \(a=l\times w,\,\,\,l=8,\,\,\,a=48\) show answer the width is 6 meters., \(\textbf{20)}\) two numbers have a sum of 50. one number is 10 more than the other. what are the two numbers show equations \(x+y=50,\,\,\,x=y+10\) show answer the numbers are 30 and 20., \(\textbf{21)}\) a store sells jeans for $40 each and t-shirts for $20 each. in the first sale of the day, they sold 8 items in total, and the price was $260. how many of each type of item was sold show equations \(j+t=8,\,\,\,40j+20t=260\) show answer 5 jeans and 3 t-shirts were sold., \(\textbf{22)}\) the ratio of apples to carrots is 3:4. there are 28 fruits in total. how many are apples show equations \(\)a+c=28,\,\,\,4a=3c show answer there are 12 apples and 16 carrots., \(\textbf{23)}\) a phone plan costs $30 per month, and there is an additional charge of $0.10 per minute for calls. write an equation to express the cost \(c\) in terms of \(m\) minutes. show equation the equation is \(\)c=30+0.10m, \(\textbf{24)}\) a triangle has a base of 8 inches and a height of 6 inches. calculate its area. show equations \(a=0.5\times b\times h,\,\,\,b=8,\,\,\,h=6\) show answer the area is 24 square inches., \(\textbf{25)}\) a store sells shirts for $25 each and pants for $45 each. in the first sale of the day, 4 items were sold, and the price was $180. how many of each type of item was sold show equations \(t+p=4,\,\,\,25t+45p=180\) show answer 0 shirts and 4 pants were sold., \(\textbf{26)}\) a garden has a length of 12 feet and a width of 10 feet. calculate its area. show equations \(a=l\times w,\,\,\,l=12,\,\,\,w=10\) show answer the area is 120 square feet., \(\textbf{27)}\) the sum of two consecutive odd numbers is 56. what are the two numbers show equations \(x+y=56,\,\,\,x=y+2\) show answer the numbers are 27 and 29., \(\textbf{28)}\) a toy store sells action figures for $15 each and toy cars for $5 each. in the first sale of the day, 10 items were sold, and the price was $110. how many of each type of item was sold show equations \(a+c=10,\,\,\,15a+5c=110\) show answer 6 action figures and 4 toy cars were sold., \(\textbf{29)}\) a bakery sells pie for $2 each and cookies for $1 each. in the first sale of the day, 14 items were sold, and the price was $25. how many of each type of item was sold show equations \(p+c=14,\,\,\,2p+c=25\) show answer 11 pies and 3 cookies were sold., \(\textbf{for 30-33}\) two car rental companies charge the following values for x miles. car rental a: \(y=3x+150 \,\,\) car rental b: \(y=4x+100\), \(\textbf{30)}\) which rental company has a higher initial fee show answer company a has a higher initial fee, \(\textbf{31)}\) which rental company has a higher mileage fee show answer company b has a higher mileage fee, \(\textbf{32)}\) for how many driven miles is the cost of the two companies the same show answer the companies cost the same if you drive 50 miles., \(\textbf{33)}\) what does the \(3\) mean in the equation for company a show answer for company a, the cost increases by $3 per mile driven., \(\textbf{34)}\) what does the \(100\) mean in the equation for company b show answer for company b, the initial cost (0 miles driven) is $100., \(\textbf{for 35-39}\) andy is going to go for a drive. the formula below tells how many gallons of gas he has in his car after m miles. \(g=12-\frac{m}{18}\), \(\textbf{35)}\) what does the \(12\) in the equation represent show answer andy has \(12\) gallons in his car when he starts his drive., \(\textbf{36)}\) what does the \(18\) in the equation represent show answer it takes \(18\) miles to use up \(1\) gallon of gas., \(\textbf{37)}\) how many miles until he runs out of gas show answer the answer is \(216\) miles, \(\textbf{38)}\) how many gallons of gas does he have after 90 miles show answer the answer is \(7\) gallons, \(\textbf{39)}\) when he has \(3\) gallons remaining, how far has he driven show answer the answer is \(162\) miles, \(\textbf{for 40-42}\) joe sells paintings. each month he makes no commission on the first $5,000 he sells but then makes a 10% commission on the rest., \(\textbf{40)}\) find the equation of how much money x joe needs to sell to earn y dollars per month. show answer the answer is \(y=.1(x-5,000)\), \(\textbf{41)}\) how much does joe need to sell to earn $10,000 in a month. show answer the answer is \($105,000\), \(\textbf{42)}\) how much does joe earn if he sells $45,000 in a month show answer the answer is \($4,000\), see related pages\(\), \(\bullet\text{ word problems- linear equations}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- averages}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- consecutive integers}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- distance, rate and time}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- break even}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- ratios}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- age}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- mixtures and concentration}\) \(\,\,\,\,\,\,\,\,\), linear equations are a type of equation that has a linear relationship between two variables, and they can often be used to solve word problems. in order to solve a word problem involving a linear equation, you will need to identify the variables in the problem and determine the relationship between them. this usually involves setting up an equation (or equations) using the given information and then solving for the unknown variables . linear equations are commonly used in real-life situations to model and analyze relationships between different quantities. for example, you might use a linear equation to model the relationship between the cost of a product and the number of units sold, or the relationship between the distance traveled and the time it takes to travel that distance. linear equations are typically covered in a high school algebra class. these types of problems can be challenging for students who are new to algebra, but they are an important foundation for more advanced math concepts. one common mistake that students make when solving word problems involving linear equations is failing to set up the problem correctly. it’s important to carefully read the problem and identify all of the relevant information, as well as any given equations or formulas that you might need to use. other related topics involving linear equations include graphing and solving systems. understanding linear equations is also useful for applications in fields such as economics, engineering, and physics., about andymath.com, andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. if you have any requests for additional content, please contact andy at [email protected] . he will promptly add the content. topics cover elementary math , middle school , algebra , geometry , algebra 2/pre-calculus/trig , calculus and probability/statistics . in the future, i hope to add physics and linear algebra content. visit me on youtube , tiktok , instagram and facebook . andymath content has a unique approach to presenting mathematics. the clear explanations, strong visuals mixed with dry humor regularly get millions of views. we are open to collaborations of all types, please contact andy at [email protected] for all enquiries. to offer financial support, visit my patreon page. let’s help students understand the math way of thinking thank you for visiting. how exciting.

## How Do You Write and Solve an Equation From a Word Problem?

Word problems are just math in disguise! Follow along with this tutorial to get some practice translating a word problem into a mathematical equation. Then, see how to solve that equation and answer the word problem!

- word problem
- write equation
- solve variable
- define variables

## Background Tutorials

Using rates and unit rates.

## What are Rates and Unit Rates?

Can you do 100 sit-ups in 2 minutes? That's a rate! Driving a car going 40 miles per hour? That's a unit rate! Watch this tutorial to learn about rate and unit rate (and the difference!).

## Evaluating Expressions

## What is a Variable?

You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

## What's the Order of Operations?

Check out this tutorial where you'll see exactly what order you need to follow when you simplify expressions. You'll also see what happens when you don't follow these rules, and you'll find out why order of operations is so important!

## Translating Between Words and Math

## How Do You Write an Equation From a Word Problem?

One of the challenges of solving a word problem is first turning those words into a math equation you can then use to solve. This tutorial takes you through a word problem and shows you how to translate it into a useable math equation!

## Further Exploration

Solving equations by adding.

## How Do You Solve a Word Problem with an Equation Using Addition?

Word problems are a great way to see math in action! See how to translate a word problem into an equation, solve to find the answer, and check your found answer all in this tutorial.

- Terms of Use

## Get step-by-step explanations

## Graph your math problems

## Practice, practice, practice

## Get math help in your language

- Two-step equations – word problems

Simply put, two-step equations – word problems are two step equations expressed using words instead of just numbers and mathematical symbols. They are just a bit more complicated than one-step equations with word problems and they demand just a bit more effort to solve. If you are not confident in your abilities to solve two-step equations with word problems, you can go to one-step equations – word problems and practice some more before continuing with this lesson. But if you feel ready, we will show you how to solve it using this example:

Hermione’s Bikes rents bikes for $10 plus $4per hour. Janice paid $30 to rent a bike. For how many hours did she rent the bike?

First thing we have to do in this assignment is to find the variable and see what its connection is with the other values. The thing we do not know is the number of hours Janice rented the bike for and we have been asked to find that out. That means the number of hours is our variable.

The cost of renting a bike is 10$ to take the bike and 4$ for every hour it spends in our possession. The final sum Janice paid is $30. Let us write that down as an equation.

4 * x + 10 = 30

Now, in order to make things neater and more clear, let us move all the numbers (except for the number 4 – we have to get rid of it in a different way) to the right side of the equation. Like this:

4 * x = 30 – 10

To simplify things further, let us perform the subtraction.

The next thing to do is to get rid of the number 4 in front of the variable. We will do that by dividing the whole equation by 4.

4 * x = 20 |:4

Now that we have calculated the value of the variable, we can tell that Janice rented that bike for 5 hours. If you want to check the result – you can. If you multiply $4 that Janice paid per hour by the 5 hours she spend with that bike and then add the $10 she had to pay regardless of the time she spent with the bike, you will get a total sum of $30 that is indeed the full sum she paid.

These word problems are called two-step because you have to perform two mathematical operations in order to solve them. In this case – addition (subtraction) and multiplication (division). To practice solving two-step equations – word problems, feel free to use the worksheets below.

## Two-step equations – word problems exams for teachers

Two-step equations – word problems worksheets for students.

## Basic Mathematical Operations

- Addition and subtraction
- Multiplying
- Divisibility and factors
- Order of operations
- Greatest common factor
- Least common multiple
- Squares and square roots
- Naming decimal places
- Write numbers with words
- Verbal expressions in algebra
- Rounding numbers
- Convert percents, decimals and fractions
- Simplifying numerical fractions
- Proportions and similarity
- Calculating percents
- The Pythagorean theorem
- Quadrilaterals
- Solid figures
- One-step equations
- One-step equations – word problems
- Two-step equations
- Multi-step equations
- Multiplying polynomials
- Inequalities
- One-step inequalities
- Two-step inequalities
- Multi-step inequalities
- Coordinates
- Graphing linear equations
- The distance formula

## Linear Equations

- Writing a linear equation
- Systems of linear equations
- Linear systems – word problems

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## Solving Systems of Equations Real World Problems

Wow! You have learned many different strategies for solving systems of equations! First we started with Graphing Systems of Equations . Then we moved onto solving systems using the Substitution Method . In our last lesson we used the Linear Combinations or Addition Method to solve systems of equations.

Now we are ready to apply these strategies to solve real world problems! Are you ready? First let's look at some guidelines for solving real world problems and then we'll look at a few examples.

## Steps For Solving Real World Problems

- Highlight the important information in the problem that will help write two equations.
- Define your variables
- Write two equations
- Use one of the methods for solving systems of equations to solve.
- Check your answers by substituting your ordered pair into the original equations.
- Answer the questions in the real world problems. Always write your answer in complete sentences!

Ok... let's look at a few examples. Follow along with me. (Having a calculator will make it easier for you to follow along.)

## Example 1: Systems Word Problems

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

1. Let's start by identifying the important information:

- hot dogs cost $1.50
- Sodas cost $0.50
- Made a total of $78.50
- Sold 87 hot dogs and sodas combined

2. Define your variables.

- Ask yourself, "What am I trying to solve for? What don't I know?

In this problem, I don't know how many hot dogs or sodas were sold. So this is what each variable will stand for. (Usually the question at the end will give you this information).

Let x = the number of hot dogs sold

Let y = the number of sodas sold

3. Write two equations.

One equation will be related to the price and one equation will be related to the quantity (or number) of hot dogs and sodas sold.

1.50x + 0.50y = 78.50 (Equation related to cost)

x + y = 87 (Equation related to the number sold)

4. Solve!

We can choose any method that we like to solve the system of equations. I am going to choose the substitution method since I can easily solve the 2nd equation for y.

5. Think about what this solution means.

x is the number of hot dogs and x = 35. That means that 35 hot dogs were sold.

y is the number of sodas and y = 52. That means that 52 sodas were sold.

6. Write your answer in a complete sentence.

35 hot dogs were sold and 52 sodas were sold.

7. Check your work by substituting.

1.50x + 0.50y = 78.50

1.50(35) + 0.50(52) = 78.50

52.50 + 26 = 78.50

35 + 52 = 87

Since both equations check properly, we know that our answers are correct!

That wasn't too bad, was it? The hardest part is writing the equations. From there you already know the strategies for solving. Think carefully about what's happening in the problem when trying to write the two equations.

## Example 2: Another Word Problem

You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?

- 3 soft tacos + 3 burritos cost $11.25
- 4 soft tacos + 2 burritos cost $10.00

In this problem, I don't know the price of the soft tacos or the price of the burritos.

Let x = the price of 1 soft taco

Let y = the price of 1 burrito

One equation will be related your lunch and one equation will be related to your friend's lunch.

3x + 3y = 11.25 (Equation representing your lunch)

4x + 2y = 10 (Equation representing your friend's lunch)

We can choose any method that we like to solve the system of equations. I am going to choose the combinations method.

5. Think about what the solution means in context of the problem.

x = the price of 1 soft taco and x = 1.25.

That means that 1 soft tacos costs $1.25.

y = the price of 1 burrito and y = 2.5.

That means that 1 burrito costs $2.50.

Yes, I know that word problems can be intimidating, but this is the whole reason why we are learning these skills. You must be able to apply your knowledge!

If you have difficulty with real world problems, you can find more examples and practice problems in the Algebra Class E-course.

## Take a look at the questions that other students have submitted:

Problem about the WNBA

Systems problem about ages

Problem about milk consumption in the U.S.

Vans and Buses? How many rode in each?

Telephone Plans problem

Systems problem about hats and scarves

Apples and guavas please!

How much did Alice spend on shoes?

All about stamps

Going to the movies

Small pitchers and large pitchers - how much will they hold?

Chickens and dogs in the farm yard

- System of Equations
- Systems Word Problems

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- x^4-5x^2+4=0
- \sqrt{x-1}-x=-7
- \left|3x+1\right|=4
- \log _2(x+1)=\log _3(27)
- 3^x=9^{x+5}
- What is the completing square method?
- Completing the square method is a technique for find the solutions of a quadratic equation of the form ax^2 + bx + c = 0. This method involves completing the square of the quadratic expression to the form (x + d)^2 = e, where d and e are constants.
- What is the golden rule for solving equations?
- The golden rule for solving equations is to keep both sides of the equation balanced so that they are always equal.
- How do you simplify equations?
- To simplify equations, combine like terms, remove parethesis, use the order of operations.
- How do you solve linear equations?
- To solve a linear equation, get the variable on one side of the equation by using inverse operations.

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## Google Launches New Search Tools To Help With Math & Science

Google unveils new search tools to assist students with solving math, science, and visual learning problems.

- Google launched new search features to help with math, science, and visual learning.
- The updates provide step-by-step solutions for math problems and science word problems.
- New 3D interactive diagrams allow deeper exploration of STEM concepts visually.

Google is rolling out new capabilities to Search and Lens that will assist in solving complex math and science problems.

These new tools provide step-by-step explanations, solutions, and interactive 3D models to aid visual learning for STEM (science, technology, engineering, and math) subjects.

The announcement highlights new AI advancements powering the upgraded math, science, and visual search capabilities.

## Enhanced Math Problem Solving

For math questions, you can now take a snapshot of handwritten equations using the Lens app on smartphones.

This recognizes the handwriting and provides step-by-step work to reach the solution.

The new math solver tool breaks down complex calculus and trigonometry problems. It shows each step needed to get to the answer.

It’s designed to help students understand the fundamentals behind solving equations, which they wouldn’t receive by searching for the final numeric solutions online.

## Assisting With Science Word Problems

A new physics word problem feature allows you to input a question, and then it draws boxes around known variables and circles the unknowns. It then suggests relevant formulas and how to apply them correctly.

This tool currently handles foundational high school physics topics like forces, energy, and motion. Google plans to expand it to more advanced university-level concepts.

## Interactive 3D Concept Diagrams

New interactive 3D concept diagrams cover STEM topics, including cell biology, anatomy, robotics, space physics, geology, and more.

You can zoom, rotate, and click on labeled parts of each model to get definitions and detailed explanations.

The visual models aim to boost curiosity and learning of science concepts.

“Developing a deep visual understanding of STEM-related topics is a key part of mastering the subject,” Google stated.

## Providing an Intuitive Learning Experience

Google expressed hope that the math, science, and visual capabilities will enable users to satisfy their curiosity and gain new knowledge.

The features are the latest in the company’s ongoing efforts to improve Search and Lens as helpful learning tools.

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## write the equation for each word sentence and solve 2 problems. problem one : 12 more than a number is 20 problem two: The sum of a number and eight equals the sum of four times the number and six.

1. 12 + x = 20 2. x + 8 = 4x + 6

Step-by-step explanation:

problem 1 :

12 + x = 20

x + 8 = 4x + 6

## 📚 Related Questions

- Find the surface area of the triangular prism

If f(x) = -5x – 4 and g(x) = -3x -2, find (f+g)(x).

f(x) = -5x – 4

g(x) = -3x -2

(f+g)(x) = -5x – 4 + -3x -2

Combine like terms

= -8x -6

- write the expression fourteen added to the product of seven and a number

Step-by-step explanation: Because we have 14 added to something, we will need a + to whatever we are adding to. The product of 7 and a number is 7 ×x because product is the number you get after multiplication. So we get 7×x+14. You dont need parenthesis

Hope this helps!

Tell which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers. 26 Select all that apply. O A. rational numbers B. natural numbers I c. irrational numbers D. integers E. whole numbers OF. real numbers

26 can be also written as 26/1 or 52/2 or ...

so, it is part of the rational numbers.

it is clearly a natural number (1, 2, 3, 4, ...).

it is also an integer (... , -2, -1, 0, 1, 2, 3, ...).

it is a whole number (0, 1, 2, 3, 4, ...)

and it is a real number, as it can be written as 26.0. real numbers are the superset of all these mentioned sets of numbers.

but it is NOT an irrational number, as they have infinite digits after the decimal point without any repeating pattern.

in other words, any number that is a member of the rational numbers cannot be an irrational number. and vice versa.

Details : Tell which set or sets the number below belongs to: natural numbers,

The table shows the relationship between the number of white shells and the number of pink beads that Aliz uses to decorate 6 different jewelry box. Which of the following equations relates the number of pink beads, p, to the number of white shells, w? �� p = 25w �� w = 52p �� 5w = 2p �� p = 52w

We want the ratio of pink beads to white shells

Cross multiply

Divide by 2

How many solutions exist for the given equation? 3(x-2)=22-x O zero Oone Otwo Oinfinitely many

one solution

3(x-2)=22-x

3x -6 = 22-x

Add x to each side

3x-6+x = 22-x+x

Add 6 to each side

4x-6+6 = 22+6

Divide by 4

4x/4 = 28/4

There is one solution

It has only one solution

[tex]3(x - 2) = 22 - x [/tex]

open the brackets:

[tex]3x - 6 = 22 - x[/tex]

collect like terms together:

[tex]3x + x = 22 + 6[/tex]

then solve:

[tex]4x = 28 \\ x = \frac{28}{4} \\ \\ x = 7[/tex]

If 4 tickets to a show cost $17.60, what is the cost of 7 such tickets.

We can use a ratio to solve

4 tickets 7 tickets

------------------- = ----------------

17.60 dollars x dollars

Using cross products

4x = 17.60 * 7

Divide each side by 4

4x/4 = 123.2/4

Simplify 9x + 4 + 2x + 2 by combining like terms.

9x + 4 + 2x + 2

9x+2x + 4 +2

Details : Simplify 9x + 4 + 2x + 2 by combining like terms.

3 different problems. solve b - 4 = 3. solve -32 = 8w solve n — = -4 7

Add 4 to each side

b - 4+4 = 3+4

Divide by 8

-32/8 = 8w/8

Multiply by 7 to each side

n/7 *7 = -4*7

A motel has 20 rooms. If the manager charges $60 per room per night, all the rooms will be rented. For each $5 increase, one less room will be rented. How much rent should be charged to maximize revenue? What is the maximum revenue?

Revenue: $1280

We can solve this by representing the problem as an expression and finding the maximum of that

We know that revenue = number of sales * average price. If x represents the amount of 5 dollar increases, then we subtract x from 20 to get the total number of sales. For example, if there was 1 5 dollar increase, the number of sales would be 20-1 = 19. Similarly, the average price is equal to 60 + 5x, as we add $5 for each x. For example, if there were 3 $5 increases, it would cost 60 + 3 * 5 = 75 per room.

revenue = (20-x) * (60 + 5x)

= 1200 + 100x - 60x - 5x²

= -5x²+40x+1200

This is a quadratic expression -- we know it is one because it is of form ax²+bx+c, where a=-5, b=40, and c = 1200. Because the a is negative, the quadratic expression (which forms a parabola) opens downward, meaning that there is a peak of the expression at its vertex.

The x value of the vertex of a parabola given this form for the quadratic expression is (-b/2a) , which is (-40/(2*(-5))) = -40/-10 = 4 here, and plugging that into our equation,

y= -5x²+40x+1200

= -5 (4)²+40(4) + 1200

= -5 * 16 + 160 + 1200

= 1280 as our maximum revenue

Therefore, the amount of 5 dollar increases is 4, making the average price equal to 60 + 5 * 4 = 80 dollars

You can Figure A to map it onto Figure Din a single transformation." 1.answers 2.rotate 3.reflect 4.translate 5.dilate

Find the value of x for which l||m

The angles are correcting angle and corresponding angles are equal when the lines are parallel

Subtract 25 from each side

55-25 = x+25

Details : Find the value of x for which l||m

Given the equation, 1 + 6k = 25, for some value of k, what is the value of k +7 for the same value of k?

c o l l e c t l i k e t e r m s

1 - 2 5 = 6 k

- 2 4 = 6 k

d i v i d e b o t h s i d e s b y 6

; - k = - 4

is three a solution of z^2 +1=4+3z?

z^2 +1=4+3z

Substitute into the equation and see if it is true

3^2 +1 = 4+3(3)

This is not a true statement so this is not a solution

Please help me I’m confused

A midpoint is a point that divides a given line into two equal halves .The answers to the questions are:

2. The coordinate of I is 2.5

A line segment can be divided into different fractions . Where the point that divides the line segment into equal parts is the midpoint . however, number line is a system that shows the location or positions of all directed numbers.

The given questions can be solved as follows:

1. Given that point A is between BC and AB = 4x -3, BC = 7x + 5, AC = 5x - 16

BC = AB + AC

7x + 5 = (4x -3) + (5x - 16)

= 9x - 19

7x + 5 = 9x - 19

19 + 5 = 9x - 7x

x = [tex]\frac{24}{2}[/tex]

a. BC = 7x + 5

= 7(12) + 5

The value of BC is 89 .

b. AB = 4x -3

= 4(12) - 3

Thus AB has a value of 45 .

c. AC = 5x - 16

= 5(12) -16

The value of AC is 44 .

2. Given that H is the mid point of GI , and G = 8, I = -3.

The coordinate of I is 2.5

3. A midpoint is a point that divides a line segment in to two equal halves . Given that J is the midpoint of KL . KL = 38

J = [tex]\frac{KL}{2}[/tex]

= [tex]\frac{38}{2}[/tex]

The value of the midpoint J is 19 .

4. It can be deduced from the conditions given in the question that:

MQ = MN + NO + OP + PQ

= 8 + 8 + 16 (NB: OP + PQ = 16)

Thus, value of MQ is 32 .

5. Since P is the mid point of NQ , and OP = 11, OQ = 35

PQ = OQ - OP

= 35 - 11

Since, PQ = NP =24

NO = NP - OP

= 24 - 11

NO has a length of 13 .

6. NO = 2y + 11, OP = 3y - 2, NP = 6y + 3 and MP = 64.

NO + OP = NP

(2y + 11) + (3y - 2) = 6y + 3

5y + 9 = 6y + 3

9 - 3 = 6y - 5y

a. NO = 2y + 11

= 2(6) + 11

Here, the value of NO is 23 .

b. MN = MP - NP

NP = 6y + 3

= 6(6) + 3

MN = 64 - 39

So that MN has a value of 25 .

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How many subsets are there in {p, e, t}?

Number of subset= [tex]2^{n}[/tex]

Her, n is the number of elements in the set.

{p , e , t}

Number of subset = 2³ = 2 * 2 *2 = 8

Details : How many subsets are there in {p, e, t}?

Your mom asks you to transfer the rice in the pantry from the plastic sack it comes in to a rectangular storage container. The first container is 4 inches wide, 4 inches deep, and 12 inches high. The second container is 5 inches wide, 5 inches deep, and 8 inches high. Calculate the volume of both containers. Which container will hold more rice?

something amazing

pls answer i will mark brainliest

In terms of price;

[tex]2x + \frac{5}{2} y = 19 \\ \\ 4x + 5y = 38 - - - (equation \: \: 1)[/tex]

In terms of people, each person will get one snack:

[tex]x + y = 8 - - - (equation \: \: 2)[/tex]

[tex]in \: equation \: 2 : \\ x = 8 - y \\ substitute \: for \: x \: in \: 1 : \\ 4(8 - y) + 5y = 38 \\ 32 - 4y + 5y = 38 \\ y = 6 \\ \\ therefore : x = 2[/tex]

Sam bought 2 bags of chips

(3,y) (1,4) m= -2 what is the value of y if the line through the two given points is to have indicated slope

The equation for the slope is

m = ( y2-y1)/(x2-x1)

-2 = (4-y)/(1-3)

-2 = (4-y)/-2

Multiply each side by -2

Subtract 4 from each side

4-4 = 4-y-4

Factor the polynomial completely using the X method. x2 + 16x + 48 An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression x squared + 16 x + 48.

The factors of the polynomial x² + 16x + 48 are ;

-4 and -12.

Given the polynomial :

x² + 16x + 48

To factorize :

x² + 16x + 48 = 0

Two numbers whose addition gives 16 and product gives 48

The two numbers are : 12 and 4

x² + 12x + 4x + 48 = 0

x(x + 12) + 4(x + 12)

(x + 12) = 0

(x + 4) = 0

x = -4 or x = -12

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Details : Factor the polynomial completely using theX method.x2 + 16x + 48

Is 3.739 rational or irrational

It is a rational number.

A rational number is a number that repeats with the same number, or terminates. An irrational number is a number that repeats, but not with a constant number, like pi for example. 3.739 terminates at the end, so it is a rational number.

Hope this helps :)

what is the bionomial expansion of (x-1y)^2

[tex] {(x - y)}^{2} \\ = (x - y)(x - y)[/tex]

[tex] = ( {x}^{2} - xy - xy + {y}^{2} ) \\ = {x}^{2} - 2xy + {y}^{2} [/tex]

Which equation represents a parabola that has a focus of (0,0) and a directix of y = 2?

[tex]a=0,\ b=0,\ k=2\\equation\ of\ the\ parabola:\\\\y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\\\y=-\dfrac{x^2}{4}+1 \\\\x^2=-4(y-1)\\\\Answer\ D[/tex]

Which of these expressions is equivalent to 4m + 8m? A. 32m B. 12m2 C. 32m2 D 12m

Answer: D. 12m

They are both like terms so they can be added

Details : Which of these expressions is equivalent to 4m + 8m?A.32mB.12m2C.32m2D12m

The midpoint of line segment AB is (-2,1). If the coordinates of B are (0,2) what are the coordinates of A?

The required coordinate of A will be at (-4, 0)

When a point bisects a line , it cuts the line into two equal part s and the point on that line is known as its midpoint . The expression for calculating the midpoint of a line is expressed as;

[tex]M(X, Y)= [{ \frac{x_2+x_1}{2} , \frac{y_2+y_1}{2} ][/tex] where:

[tex]X =\frac{x_2+x_1}{2} \\Y=\frac{y_2+y_1}{2}[/tex]

From the question, we are given the following coordinate points

[tex]X=-2\\x_1=0\\[/tex]

[tex]X =\frac{x_2+x_1}{2}\\-2 =\frac{x_2+0}{2}\\2 \times -2=x_2+0\\-4=x_2\\ Swap\\x_2=-4\\[/tex]

[tex]Y =\frac{y_2+y_1}{2}\\1 =\frac{y_2+2}{2}\\2 \times 1=y_2+2\\2=y_2+2\\y_2=2-2\\y_2=0[/tex]

Hence the coordinate of A will be (-4, 0)

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The midpoint of line segment AB is (1,2). if the coordinates of A are (1,0) what are the coordinates of B

The required coordinate of B will be at (1, 4)

[tex]X=1\\x_1=1\\[/tex]

[tex]X =\frac{x_2+x_1}{2}\\1 =\frac{x_2+1}{2}\\2=x_2+1\\x_2=2-1\\x_2=1\\[/tex]

[tex]Y =\frac{y_2+y_1}{2}\\2 =\frac{y_2+0}{2}\\2 \times 2=y_2+0\\4=y_2+0\\y_2=4\\[/tex]

Hence the coordinate of B will be (1, 4)

I met this hella weird cryptic dude who interviewed me and gave me this puzzle. Solve it within 12 hours and ill let you know what he says. Row zero (0) must be solved. Your final code should contain nine (9) letters, and one (1) number. The number two (2) has been given to you as the first character in your final code. Disclaimer: This code is foreign, meaning it is not a word or sentence from any language. It is a string of specific characters. You will be given a second, simpler cipher to decrypt that reads "graph." It has already been solved for you. Understanding how this smaller chart produces "graph" will grant you the deciphering method used for the large cipher. This cipher must be completed at maximum twenty-four (24) hours from reception. Failure to complete in this time will result in re-calibration via interviewing, not disqualification, should you (as a participant) wish to continue. To validate this code, or request further clarification, refer to this account. Speaking to any personnel regarding the cipher without supervision is strictly prohibited, and will result in disqualification. HINTS: "^," or Carrots, signify a capitalized letter in the string. Capitalization matters. Everything you need to complete this cipher is given here. Only very basic math was used to encrypt this key (Multiplication and Division). You are not allowed to ask others for help without the supervision of the employment center. We will know if you've leaked, or gave any information out regarding this Cipher. We are entrusting you with it. Best of luck

no cheating thanks <3

order the equations by the steepness of the slopes of their graphs from greatest fj least.

Details : order the equations by the steepness of the slopes of their graphs

A textbook store sold a combined total of 255 physics and math textbooks in a week. The number of math textbooks sold was 81 less than the number of physics textbooks sold. How many textbooks of each type were sold?

physics = 168

Brainliest, please!

m = math, p = physics

m + p = 255

Substitution:

(p - 81) + p = 255

2p - 81 = 255

Solving for m:

m + 168 = 255

m = 255 - 168

Checking with the other equation:

87 = 168 - 81

So, math = 87 and physics = 168

ILL MARK BRAINIEST IF YOU DO THIS CORRECTLY!!! Drag each tile to the correct box. Order the expressions from least value to greatest value.

I think thats the answer. Check it. (:

-2.2x3.4= -74.8

42/-6= -7/10

-3 3/5-( 3 1/10)= - 21/10

-2 3/4+(3 1/6)= -2

!I might be wrong!

Someone check this!

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Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems. Show more Why users love our Word Problems Calculator Middle School Math Solutions - Equation Calculator

This compilation of a meticulously drafted equation word problems worksheets is designed to get students to write and solve a variety of one-step, two-step and multi-step equations that involve integers, fractions, and decimals. These worksheets are best suited for students in grade 6 through high school.

Solving algebraic word problems requires us to combine our ability to create equations and solve them. To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation. If the variable is not the answer to the word problem, use the variable to calculate the answer.

You might need: Calculator Mindy and Troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake and Troy had 1 4 of the total cake. Write an equation to determine how many pieces of cake ( c) there were in total. Find the total number of pieces of cake. pieces of cake Show Calculator Stuck?

How do we solve them? The trick is to break the solution into two parts: Turn the English into Algebra. Then use Algebra to solve. Turning English into Algebra To turn the English into Algebra it helps to: Read the whole thing first Do a sketch if possible Assign letters for the values Find or work out formulas

How to write word problems as equations — Krista King Math | Online math help Word problems can seem to be tricky at first. What is the problem actually asking you to do? There are certain phrases that always mean the same operation in math. The table below will help you learn common phrases in math and what operations they represent.

Solution: Adding 9 to a number is written as x + 9, while subtracting 7 from three times the number is written as 3x − 7. We therefore get the equation: x + 9 = 3x − 7. We solve for x by adding 7 on both sides of the equation: x + 16 = 3x. Then we subtract x: 16 = 2x. After dividing by 2, we obtain the answer x = 8.

Lesson 18: Word Problems Worksheet Name _____ 1. Use the structure sentence Number of boxes • Number of Items per Box = Total Number of Items to write an equation for each problem. Use a variable where necessary. You don't need to solve the equations. 2. At your wedding reception, you'll have:

Solve the problem. Check your work. We'll work through an algebra word problem using these steps. Here's a typical problem: The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost $360. How many miles did she drive?

Learn how to solve a word problem by writing an equation to model the situation. In this video, we use the linear equation 210 (t-5) = 41,790. Created by Sal Khan. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted Ryan Merritt 10 years ago Whoa, how does Sal do that complex division using MENTAL MATH?

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Show Answer 10 weeks ($155) \ (\textbf {2)}\) Mike and Sarah collect rocks. Together they collected 50 rocks. Mike collected 10 more rocks than Sarah. How many rocks did each of them collect? Show Equations \ (m+s=50,\,\,\,m=s+10\) Show Answer Mike collected 30 rocks, Sarah collected 20 rocks.

Sal solves a word problem about a ball being shot in the air. The equation for the height of the ball as a function of time is quadratic. Created by Sal Khan and Monterey Institute for Technology and Education. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted Caroline Darragh 10 years ago

What are you trying to solve for? Identify the variable: Use the statement, Let x = _____. You can replace the x with whatever variable you are using. Look for key words that will help you write the equation. Highlight the key words and write an equation to match the problem.

Word problems are a great way to see math in action! See how to translate a word problem into an equation, solve to find the answer, and check your found answer all in this tutorial. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 ...

Are those word problems not adding up? Solve the word problems by using equations. Here's how:

This test has 10 equation word problems and is a great way for students to practice solving word problems involving integers. This test has ten problems consisting of multiple choice questions, matching, and fill-in-the-blank.

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These word problems are called two-step because you have to perform two mathematical operations in order to solve them. In this case - addition (subtraction) and multiplication (division). To practice solving two-step equations - word problems, feel free to use the worksheets below.

Let y = the number of sodas sold. 3. Write two equations. One equation will be related to the price and one equation will be related to the quantity (or number) of hot dogs and sodas sold. 1.50x + 0.50y = 78.50 (Equation related to cost) x + y = 87 (Equation related to the number sold) 4. Solve!

Free equations calculator - solve linear, quadratic, polynomial, radical, exponential and logarithmic equations with all the steps. Type in any equation to get the solution, steps and graph ... Word Problems. Age Problems; Distance Problems; Cost Problems; Investment Problems; Number Problems; Percent Problems; Addition/Subtraction ...

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Mathematics High School. write the equation for each word sentence and solve 2 problems. problem one : 12 more than a number is 20. problem two: The sum of a number and eight equals the sum of four times the number and six. 1 bulan yang lalu.