Free Printable System Of Equation Word Problems

Worksheets

System Of Equation Word Problems

Total questions: 20

Worksheet time: 5hrs 50mins

Name

Class

Date

There are 15 animals in a barn. These animals are horses (x) and chickens (y). 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 (x) and 6 bananas (y) 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

Habiba sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Ruth 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?

Sugar Cookies $5
Oatmeal Cookies $3

Sugar Cookies $4
Oatmeal Cookies $8

Sugar Cookies $2
Oatmeal Cookies $6

Sugar Cookies $3
Oatmeal Cookies $6

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?

(35, 52)

(18, 69)

( 52, 35)

(61, 26)

The senior class at Orchard Collegiate High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Essex High School rented and filled 12 vans and 14 buses with 770 students. How many students were on each van and each bus?

Van 43
Bus 14

Van 11
Bus 21

Van 14
Bus 43

Van 17
Bus 45

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.

Adult $13
Child $5

Adult $10
Child $6

Adult $8
Child $16

Adult $12
Child $13

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

20 Multiple Choice

10 Multiple CHoice

15 Multiple Choice

5 multiple choice

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

Yazzy 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 Yazzy 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

10.

On Monday Jay 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

11.

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

x + y = 1550
y = 4x

x + y = 1550
y = x + 4

y - x = 1550
y = 4x

y = 1550 + x
y = x + 4

12.

Dishann mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels?

d + n = 6.60
.10d + .05n = 80

d + n = 80
d + n = 6.60

d + n = 80
.10d + .05n = 6.60

d + n = 80
.05d + .10n = 6.60

13.

At a corner store the cost for a bag of Takis and a beverage is $2.10. The cost for 2 bags and 3 bev's is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

t: # of bags of Takis b: # of beverages

t: Cost of each bag of Taki's b: Cost of each beverage

t: total cost b: # of food items

t: Cost of each beverage. b: Cost of each bag of Takis

14.

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?

y = 9.65 + x
y = 8.40 + x

y = 9.65x + 43
y = 8.40x + 58

y =9.65x
y = 8.40x

y = 9.65x - 43
y = 8.40x - 58

15.

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

Elimination

Substitution

Estimation

Graphing

16.

The sum of two numbers is 6. The difference of the two numbers is 46. Find the numbers.

46 and 52

-52 and 40

-26 and 20

-46 and 40

17.

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. How many nickels and dimes did Dennis earn?

40 nickels, 40 dimes

52 nickels, 28 dimes

28 nickels, 52 dimes

30 nickels, 50 dimes

18.

Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?

$10

$15

$20

19.

What would be the first step in finding the solution using elimination?

2x + 2y = -2

3x - 2y = 12

you cannot solve this using eliminiation

cross out the 2x and 3x

cross out the 2y and -2y

change to slope intercept form and graph

20.

Solve for x and y
y = 2x + 1
y = 4x - 1

(1,3)

(-1,-3)

(-1,3)

(3,1)

Reset

System Of Equation Word Problems

Total questions: 20

Worksheet time: 5hrs 50mins

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