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Writing Systems of equations from Word Problems - Printable Mathematics Worksheets - Wayground

Writing Systems of equations from Word Problems

8 questions

8th - 8th Grade

Mathematics

This Grade 8 mathematics worksheet helps students translate real-world word problems into systems of two linear equations. Across 8 multiple-choice questions, students identify equations for situations involving prices, quantities, totals, ticket sales, pizza costs, bills, animal legs, and coin values. The items require students to define variables and connect each statement in a scenario to either a counting or value equation. The worksheet is designed for students who are learning to represent verbal relationships algebraically before solving a system. It is useful for guided practice, independent review, homework, or a quick formative assessment of equation setup. Students receive practice distinguishing fixed costs from variable rates, matching coefficients to quantities, and using monetary values accurately. This free printable worksheet includes a complete answer key for efficient checking and feedback.

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Worksheets

Writing Systems of equations from Word Problems

Total questions: 8

Name
Class
Date
1.

Michael spent $50 for 6 tigerfish and 8 goldfish. Shaun spend $5 more than Michael for 5 tigerfish and 10 goldfish. Write a system of equations that could be use the find t, the price of a tigerfish and g, the price of a goldfish.

a)

8t+6g=508t+6g=50
10t+5g=5510t+5g=55

b)

6t+8g=506t+8g=50
5t+10g=455t+10g=45

c)

6t+8g=506t+8g=50
5t+10g=555t+10g=55

d)

8t+6g=508t+6g=50
10t+5g=4510t+5g=45

2.

Sarah enjoys cutting lawns and charges $20 for each small lawn and $30 for each large lawn she mows. Sarah earned $140 for mowing 6 lawns. Write a system of equations that could be used to find x, small lawns and y, large lawns Sarah mowed.

a)

30x+20y=14030x+20y=140
x+y=6x+y=6

b)

50(x+y)=14050\left(x+y\right)=140
x+y=6x+y=6

c)

20x+30y=14020x+30y=140
x+y=6x+y=6

d)

x+y=140x+y=140
x+y=6x+y=6

3.

The drama club is selling tickets to its play. The cost of an adult ticket is $4.50, and the cost of a student ticket is $2.50. The theater can hold 250 people and they want to make $1,005. Write a system of equations that could be used to find x, the number of adult tickets and y, the number of student tickets.

a)

4.50x+2.50y=1,0054.50x+2.50y=1,005
x+y=250x+y=250

b)

4.50x+2.50y=2504.50x+2.50y=250
x+y=1,005x+y=1,005

c)

2.50x+4.50y=1,0052.50x+4.50y=1,005
x+y=250x+y=250

d)

2.50x+4.50y=2502.50x+4.50y=250
x+y=1,005x+y=1,005

4.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings (x) when both companies cost (y) the same amount?

a)

y = 6.80 + .65x

y=7.30+.90x

b)

x + y = 6.80

x + y = 7.30

c)

y = 6.80+.90x

y = 7.30 + .65x

d)

y + .90x = 6.80

y + .65x = 7.30

5.

Nancy went to the grocery story. 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

6.

Caitlin won a bag full of money at the fundraiser party! She won 49 bills that amounted to $1430. The bills consist of twenty dollar bills and fifty dollar bills. Using x for number of $20 bills and y for number of $50 bills, which systems would help determine how many of each bill Caitlin has?

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

7.
There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?
a)
x + y = 15
4x + 2y = 44
b)
4x + 2y = 15
x + y = 44
c)
x = 2y + 44
4x = y + 15
d)
2x - 4y = 44
x - y = 15
8.

Tania had 35 coins in pennies and nickels. She had $1.03. Which system of equations could be used to determine the number of coins she has?

a)

.01p + .05n = 35

p + n = 103

b)

1p + 5n = 1.03

p + n = 35

c)

.01p + .05n = 1.03

p + n = 35

d)

.05p + .01n = 1.03

p + n = 35

Answer Key

Writing Systems of equations from Word Problems

Total questions: 8

1.
c)

6t+8g=506t+8g=50
5t+10g=555t+10g=55

2.
c)

20x+30y=14020x+30y=140
x+y=6x+y=6

3.
a)

4.50x+2.50y=1,0054.50x+2.50y=1,005
x+y=250x+y=250

4.
c)

y = 6.80+.90x

y = 7.30 + .65x

5.
c)

4x + 6y = 13

3x + 7y = 13.5

6.
c)

x + y = 49

20x + 50y = 1430

7.
a) x + y = 15
4x + 2y = 44
8.
c)

.01p + .05n = 1.03

p + n = 35

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FAQs

What does this worksheet cover, and how does it help students write systems of equations?

This Grade 8 worksheet focuses on representing word problems as systems of two linear equations rather than solving the systems. Its 8 multiple-choice items ask students to define variables and match real-world relationships—such as ticket totals and revenue, item counts and prices, or animal counts and legs—to correctly structured equations. Completing the questions builds the translation skill needed before solving systems algebraically.

How can I use this worksheet to teach writing systems of equations from word problems?

Introduce a consistent process: name the variables, identify the two quantities or conditions, and write one equation for each condition before reviewing the answer choices. Use the ticket, coin, or animal-leg problems to model how a total-number equation differs from a total-value equation. Then have students explain why coefficients such as 4.50 and 2.50 represent ticket prices, while 250 represents the total number of tickets.

What mistakes should I watch for when students complete this systems-of-equations worksheet?

Watch for students reversing the meaning of variables, using a total amount where a total count belongs, or omitting a coefficient. Common errors include writing 20x + 50y = 49 instead of using 49 for the number of bills, treating animal legs as two equal quantities, and confusing a pizza's base cost with its per-topping rate. In the coin and grocery problems, students may also mix up dollar values and item counts or misplace decimal amounts.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can use the 8 multiple-choice questions for independent practice or assessment. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so the word-problem text and multiple-choice systems are easier to scan. You can also apply a dyslexia-friendly font or translate the worksheet text into another language. These options can make the price, count, and total relationships in each problem more accessible without changing the equation-writing focus.

Where can I find more 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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