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Systems of Equations Word Problem

Total questions: 20

Worksheet time: 20mins

Name
Class
Date
1.

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

2.

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

3.

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?

a)

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

b)

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

c)

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

d)

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

4.

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

a)

t + n = 54
t = 3n + 8

b)

t + n = 54
n = 3t + 8

c)

t + n = 54
t = 3n - 8

d)

t + n = 8
t = 3n + 54

5.

A sporting goods store sells left haded (x) and right handed (y) gloves. In one month, 12 gloves were sold for a total of $561. Right handed gloves cost $45 each and left handed gloves cost $52. Which system could be solved to determine the number of each type of glove sold?

a)

x + y = 561

45x + 52y = 12

b)

x + y = 12

52x + 45y = 561

c)

x + y = 12

45x + 52y = 561

d)

x + y = 561

52x + 45y = 12

6.

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

a)

x + y = 6
14.80x + 17y = 91

b)

x + y = 91
14.80x + 17y = 6

c)

x + y = 6
14.80y + 17x = 91

d)

x + y = 91
14.80x+ 17y = 6

7.

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

a)

5q + 2z = 1.32
1z = 0.75

b)

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

c)

q + z = 1.32
q + z = 0.75

d)

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

8.

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

9.

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?

a)

x + y = 1550
y  = 4x

b)

x + y = 1550
y = x + 4

c)

y - x = 1550
y = 4x

d)

y = 1550 + x
y = x + 4

10.

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

a)

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

b)

x = -2
y = 5

c)

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

d)

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

11.
a)
b)
c)
d)
12.

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

13.

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?

a)

x + y = 1550

y = 4x

b)

x + y = 1550

y = x + 4

c)

y - x = 1550

y = 4x

d)

y = 1550 + x

y = x + 4

14.

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

a)

1s + 3c = 38

2s + 3c = 52

b)

3s + 1c = 38

3s + 2c = 52

c)

s + c = 38

s + c = 52

d)

3s + 3c = 38

1s + 2c = 52

15.

A boy has seven more nickels than quarters. The total value of the coins is $4.90. Which system could be used to find out how many nickels and quarters he has?

a)
b)
c)
d)
16.

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

17.

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

18.

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.  Which system of equations could be used to find the exact number of dimes and nickels? 

a)

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

b)

d + n = 80
d + n = 6.60

c)

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

d)

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

19.

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. If a system of equations is written, which would be the correct representation of the 2 variables?

a)

t: # of tacos
m: # of glasses of milk

b)

t: Cost of each taco
m: Cost of each glass of milk

c)

t: total cost
m: # of food items

d)

t: Cost of each glass of milk
m: Cost of each taco

20.

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