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Systems of Equations Word Problems - Printable Mathematics Worksheets - Wayground

Systems of Equations Word Problems

18 questions

8th - 8th Grade

Mathematics

This free printable worksheet helps Grade 8 students model and solve systems of equations in real-world contexts. Across 18 multiple-choice questions, students translate information about prices, ticket sales, ages, bills, quantities, and rates into two linear equations, identify the correct system, solve for both variables, and interpret an ordered-pair solution in context. The worksheet also checks students’ understanding of substitution, elimination, and graphing as solution methods, including recognizing an intersection point as a meaningful answer. It is useful for guided practice, independent review, homework, or a formative assessment after introducing systems of equations word problems. A complete answer key is included, making it easier to review equation setup, solution accuracy, and the meaning of each answer. Teachers can use the free printable PDF or assign the digital version through Wayground.

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Systems of Equations Word Problems

Total questions: 18

Name
Class
Date
1.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

a)

4y = 3x + 64

8y = x + 68

b)

4y = 3x + 64

8y = x + 60

c)

3x + 4y = 64

x + 8y = 68

d)

3x + 4y = 64

x + 8y = 60

2.
Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?
a)
3x + 2y = 315
2x + 4y = 450
b)
3x + 2y = 450
2x + 4y = 315
c)
2x + 2y = 315
3x + 4y = 450
3.
On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 
a)
10c + 5d = 14.25
5c + 10d = 16.50
b)
10c + 5d = 16.50
5c + 10d = 14.25
c)
c + d = 10
5c + 10d = 16.50
d)
c + d = 5
5c + 10d = 16.50
4.
Solve the system of equations.
y = 4x+1
3x + 2y = 13
a)
(1, 5)
b)
(5, 1)
c)
(0.25, 2)
d)
∅
5.

The brown bunny (x) ate 22 carrots more than the white bunny (y). The bunnies together had eaten a total of 60 carrots during the week. How many carrots did each bunny eat?

a)

x + y = 22

x = y + 60

b)

x + y = 60

x = y + 22

c)

x + y = 22

y = x - 22

d)

2x + y = 22

x = y + 60

6.
Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount? 
a)
y = 9.65 + x
y = 8.40 + x
b)
y = 9.65x + 43
y = 8.40x + 58
c)
y =9.65x
y = 8.40x
d)
y = 9.65x - 43
y = 8.40x - 58
7.
Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?
a)
4x + 7y = 578
x + y = 3365
b)
4x + 7y = 3365
x + y = 578
c)
4y + 7x = 578
x + y = 3365
d)
4y + 7x = 3365
x + y = 578
8.

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total.


To solve, I graphed:

x + y = 21

6x + 4y = 104


I got an intersection point at (10,11). What does that mean in context of the problem?

a)

There are 10 adults and 11 children.

b)

There are 11 adults and 10 children.

c)

The adults are $10 and the children are $11.

d)

There are 104 adults and 21 children.

9.
Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.
a)
x + y = 33
y = 2x - 3
b)
x + y = 33
x = 2y - 3
c)
x + y = 33
x = 3 - 2y
d)
x + y = 3
x = 33 - 2y
10.
Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 
a)
x + y = 1430
20x + 50y = 49
b)
x + y = 49
10x + 5y = 1430 
c)
x + y = 49
20x + 50y = 1430
d)
x + y = 49
x + y = 1430
11.
The sum of Mr. Micklow and Ms. Craft's age is 55.  The difference is 3.  
Solve:
x + y = 55
x - y = 3
a)
(26, 23)
b)
(26, 29)
c)
(29, 26)
d)
(29, 32)
12.
Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?
a)
Sugar Cookies $5 
Oatmeal Cookies $3
b)
Sugar Cookies $4
Oatmeal Cookies $8
c)
Sugar Cookies $2
Oatmeal Cookies $6
d)
Sugar Cookies $3
Oatmeal Cookies $6
13.

Which of the following is not a method for solving systems of equations

a)

Elimination

b)

Substitution

c)

Estimation

d)

Graphing

14.
On the first night, the Movie House Theater sold 7 adult tickets and 11 child tickets for $227. On the second night they took in $150 by selling 6 adult tickets and 6 child tickets. Find the price of an adult ticket and the price of a child ticket.
a)
Adult $13
Child $5
b)
Adult $10
Child $6
c)
Adult $8
Child $16
d)
Adult $12
Child $13
15.
Two small pitchers and one large pitcher can hold 8 cups of water.  One large pitcher minus one small pitcher constitutes 2 cups of water.  How many cups of water can each pitcher hold?
a)
8 large, 2 small
b)
6 large, 4 small
c)
4 large, 2 small
d)
2 large, 2 small
16.

Nancy went to Ramey's to buy groceries.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

a)
4x + 6y = 3
13.5x - 13y = 6
b)
x + y = 4
x - y = 6
c)
4x + 6y = 13
3x + 7y = 13.5
d)
4x - 6y = 13
3x - 7y = 13.5
17.
David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?
a)
(35, 52)
b)
(18, 69)
c)
( 52, 35) 
d)
(61, 26)
18.

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.

Which system best represents the situation?

a)

4x + 7y = 578

x + y = 3365

b)

4x + 7y = 3365

x + y = 578

c)

4y + 7x = 578

x + y = 3365

d)

4y + 7x = 3365

x + y = 578

Answer Key

Systems of Equations Word Problems

Total questions: 18

1.
c)

3x + 4y = 64

x + 8y = 68

2.
a) 3x + 2y = 315
2x + 4y = 450
3.
b) 10c + 5d = 16.50
5c + 10d = 14.25
4.
a) (1, 5)
5.
b)

x + y = 60

x = y + 22

6.
b) y = 9.65x + 43
y = 8.40x + 58
7.
b) 4x + 7y = 3365
x + y = 578
8.
a)

There are 10 adults and 11 children.

9.
b) x + y = 33
x = 2y - 3
10.
c) x + y = 49
20x + 50y = 1430
11.
c) (29, 26)
12.
b) Sugar Cookies $4
Oatmeal Cookies $8
13.
c)

Estimation

14.
d) Adult $12
Child $13
15.
c) 4 large, 2 small
16.
c) 4x + 6y = 13
3x + 7y = 13.5
17.
a) (35, 52)
18.
b)

4x + 7y = 3365

x + y = 578

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FAQs

What does this systems of equations word problems worksheet cover?

This Grade 8 mathematics worksheet uses 18 multiple-choice questions to help students translate real-world information into systems of two linear equations and solve them. Students work with contexts such as ticket sales, prices, ages, bills, and quantities, then identify solutions and interpret ordered pairs in context.

How can I use this worksheet to teach modeling with systems of equations?

Before students begin, have them define what each variable represents and underline the two quantities or relationships provided in each word problem. Ask students to write one equation for each condition, explain why its coefficients and constant match the context, and then use substitution, elimination, or graphing to solve and check the result.

What mistakes should I watch for when students complete this worksheet?

Students may reverse the variables, swap the coefficients or totals when converting a situation into equations, or confuse the number of items with their total cost. They may also choose an ordered pair without matching its coordinates to the stated variables, or treat estimation as a valid system-solving method when the worksheet asks them to distinguish it from substitution, elimination, and graphing.

How do I assign and grade this systems of equations worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the 18 multiple-choice responses. Printable submissions can also be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this systems of equations word problems worksheet?

Because the worksheet contains dense multiple-choice word problems, you can adjust font spacing and font size to make the equations, quantities, and answer choices easier to scan. In Advanced Settings, you can also apply a dyslexia-friendly font or translate the worksheet into another language to support access to the problem statements.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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