solving word problems with systems of equations worksheet

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Solving systems of equations word problems worksheet for all problems, define variables, write the system of equations and solve variables.

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

Eric H. answered • 04/06/21

Math student - love helping other students

solving word problems with systems of equations worksheet

Katherine B. answered • 04/05/21

Flexible Tutor in a Wide Range of Subjects

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!

Patricia C. answered • 04/05/21

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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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?