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At a restaurant, the cost for a breakfast taco and a small glass of milk is \$2.10. the cost for 2 tacos and 3 small glasses of milk is \$5.15. Which pair of equations can be used to determine t, the cost of a taco, and m , the cost of a small glass of milk?

## 3 Answers By Expert Tutors

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The first step is to write the information as two equations. The variables are given to us as t 1 = cost of a taco

and m 1 = cost of a glass of milk.

In the information for both equations we're given the number of items purchased. For the first a single taco and glass of milk costs \$2.10, therefore

t 1 + m 1 = \$2.10

For the second equation we're given the cost of 2 tacos and 3 glasses of milk equals \$5.15, therefore

2t 1 + 3m 1 = \$5.15

If we want to solve for the values of t 1 and m 1 , we need to write an equation which defines one variable in terms of the other. We can do this by subtracting one equation from the other.

-(t 1 + m 1 ) = \$2.10

t 1 + 2m 1 = \$3.05

Next solve for t 1 by subtracting m 1 from both sides of the equation

-2m 1 -2m 1

t 1 = \$3.05 - 2m 1

To solve for the first variable, \$3.05 - 2m 1 can be substituted for t 1 in either equation

(\$3.05 - 2m 1 ) + m 1 = \$2.10

Combine like terms to get

\$3.05 - m 1 = \$2.10

Subtract \$3.05 from both sides of the equations

-m 1 = -\$0.95

Multiply both sides by -1 to solve for m 1, which results in

m 1 = \$0.95

Now it's possible to solve for t 1 by putting the value of m 1 into the equation for t 1

t 1 = \$3.05 - 2(\$0.95)

t 1 = \$3.05 - \$1.90

t 1 = \$1.15

Now check the answer by substituting the values of t 1 and m 1 into both equations

\$1.15 + \$0.95 = \$2.10

2(\$1.15) + 3(\$0.95) = \$5.15

\$2.30 + \$2.85 = \$5.15

Both equations are true so we have found the correct values. Hope this helps! Engineer and Mom Who Loves to Tutor Math.

t: cost of taco

m: cost of milk

1 taco and 1 glass of milk cost \$2.10, so:

t + m = 2.10

2 tacos and 3 glasses of mil cost \$5.15, so:

2t + 3m = 5.15

The system of equations is:

Solve system of equations:

m = 2.10 - t

replacing m into the second equation:

2t + 3 (2.10 - t) = 5.15

2t + 6.3 - 3t = 5.15

-1t + 6.3 = 5.15

-t = 5.15 - 6.3

replacing t into the first equation:

1.15 + m = 2.10

m = 2.10 - 1.15

The cost of a taco is \$1.15 and the cost of a glass of milk is \$0.95

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Word Problems Worksheet 1 – This 6 problem algebra worksheet will help you practice creating and solving systems of equations to represent real-life situations. You will use the “ elimination ” method to eliminate variables from standard form equations. Word Problems Worksheet 1 RTF Word Problems Worksheet 1 PDF View Answers

Word Problems Worksheet 3 – This 6 problem algebra worksheet will help you practice creating and solving systems of equations to represent real-life situations. Most of the problems involve money, so make sure you’re ready for some decimals. Word Problems Worksheet 3 RTF Word Problems Worksheet 3 PDF View Answers

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Word Problems Worksheet 6 – This 8 problem algebra worksheet features more abstract word problems like “ The sum of  twice a number, x, and twice another number, y, is 118.  The value of y is one less than twice the value of x.  Find x and y. ” One of the problems even has an infinite number of solutions! Word Problems Worksheet 6 RTF Word Problems Worksheet 6 PDF View Answers

These free  systems of equations   worksheets  will help you practice solving real-life systems of equations using the “ elimination ” method.  You will  need to create and solve a system of equations to represent each situation.  The exercises can also be solved using other algebraic methods if you choose.

This is a progressive series that starts simple with problems involving buying movie tickets and collecting for fundraisers.  Eventually the negative numbers , decimals , the  distributive property  and “ the opposite of x ” come into play.

Each worksheet will help students master Common Core skills in the Algebra strand.  They are great for ambitious students in pre-algebra or algebra classes.

These free  elmination  worksheets are printable and available in a variety of formats.  Each sheet includes an example to help you get started.  Of course, answer keys are provided as well. ## Philip Teas

There are multiple problems with your worksheets. You have word problems which are unanswerable or answers which make no sense such as fractions of people. Your answer sheets are frequently incorrect. For a quick example: System of Equations- Word Problems #1 – KEY. Question #1 states that there are 9 tickets purchased, the Answer shows a=6 and b=2. 6+2 is 8 not 9. Question 5 on that same worksheet is unanswerable. I’ve found problems on worksheet 1, 2, 5 so far. How can you claim to have the best materials with so many clear problems?

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