Free Printable Two Variable Systems

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Two Variable Systems

Total questions: 11

Worksheet time: 2hrs 6mins

Name

Class

Date

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?

1s + 3c = 38
2s + 3c = 52

3s + 1c = 38
3s + 2c = 52

s + c = 38
s + c = 52

3s + 3c = 38
1s + 2c = 52

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

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

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?

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?

3x + 2y = 315
2x + 4y = 450

3x + 2y = 450
2x + 4y = 315

2x + 2y = 315
3x + 4y = 450

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?

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

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are $20 bills and $50 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

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

10.

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

11.

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?

t + n = 54
t = 3n + 8

t + n = 54
n = 3t + 8

t + n = 54
t = 3n - 8

t + n = 8
t = 3n + 54

100 %

Two Variable Systems

Total questions: 11

Worksheet time: 2hrs 6mins

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