Free Printable System of Equations Word Problems

Worksheets

System of Equations Word Problems

Total questions: 13

Worksheet time: 49mins

Name

Class

Date

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?

x + y = 15
4x + 2y = 44

4x + 2y = 15
x + y = 44

x = 2y + 44
4x = y + 15

2x - 4y = 44
x - y = 15

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?

4x + 6y = 3
13.5x - 13y = 6

x + y = 4
x - y = 6

4x + 6y = 13
3x + 7y = 13.5

4x - 6y = 13
3x - 7y = 13.5

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. Which system of equations solves this problem to show how many students were in each van and each bus?

11v + 3b = 283

12v + 14b = 770

v + b = 14

v + b = 16

11v + 12v = 283

3b + 14b = 770

v + b = 30

23v + 17b = 1053

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

S + A = 530
3S + 4A = 1740

S + A = 530
4S + 3A = 1740

S + A = 1740
3S + 4A = 530

S + A = 1740
4S + 3A = 530

Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?

x - y = -10
x + y = -2

x = -2
y = 5

x + y = -2
x - y = -10

x + y = -10
x - y = -2

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner (x) for $14.80, and some order steak (y) for $17. If the total bill was $91, which system best represents the situation?

x + y = 6

14.80x + 17y = 91

x + y = 91

14.80x + 17y = 6

x + y = 6

14.80y + 17x = 91

x + y = 91

14.80x + 17y = 6

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

5q + 2z = 1.32
1z = 0.75

5q + 2z = 1.32
3q + 1z = 0.75

q + z = 1.32
q + z = 0.75

5q + 2z = 0.75
3q + 1z = 1.32

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?

x + y = 1430
20x + 50y = 49

x + y = 49
10x + 5y = 1430

x + y = 49
20x + 50y = 1430

x + y = 49
x + y = 1430

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?

10c + 5d = 14.25
5c + 10d = 16.50

10c + 5d = 16.50
5c + 10d = 14.25

c + d = 10
5c + 10d = 16.50

c + d = 5
5c + 10d = 16.50

10.

Which equation is "no solution" with y = 3/2x - 1?

y = -3/2x + 1

y = 2/3x - 1

y = 3/2x - 1

y = 3/2x + 2

11.

Solve the following system by using elimination:

3x - 5y = 8

2x + 5y = -3

x = 1

y = -1

x = -1

y = 1

x = 1

y = 1

x = 1

y = 0

x = 4

y = -1

12.

Solve the following system by using elimination:

-2x - 5y = -15

x + 8y = 13

x = 5

y = 1

x = 1

y = 5

x = -5

y = -1

x = 5

y = -3

x = 5

y = 2

13.

Solve by substitution:

y = -3x + 5

5x - 4y = -3

x = 1

y = 2

x = 1

y = 8

x = 2

y = -1

no solution

x = 3

y = -4

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System of Equations Word Problems

Total questions: 13

Worksheet time: 49mins

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