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Worksheets

Systems of Equations Word Problems

Total questions: 20

Worksheet time: 3600secs

Name
Class
Date
1.
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
2.
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
3.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 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

4.
What is the solution to this system of equations?
a)
(1,4)
b)
(4,1)
c)
(3,5)
d)
(-1, 4)
5.

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.  Write a system of equations for this scenario.

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
6.
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
7.

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

a)

Elimination

b)

Substitution

c)

Estimation

d)

Graphing

8.

The sum of two numbers is 28. The difference of the two numbers is 2. What are the two numbers? What equation reflects this scenario?

a)

x + y = 2

x - y = 28

b)

x + y = 28

x - y = 2

c)

28 + x = y

x - y = 2

d)

28 + x = y

x + y = 2

9.
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
10.

Your family goes to a concert. There are 6 people in your family. The adult tickets cost $14.80, and the student tickets cost $17. If the total cost 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

11.

The sum of two numbers is 30. The difference of the two numbers is 6. Write a system of equations for this scenario.

a)

x + y = 30

x - y = 6

b)

x + y = 6

x - y = 30

c)

30 + x = 6

6 - y = x

d)

30 + 6 = x

x + y = 30

12.

A vending machine has nickels and dimes. The vending machine has 32 coins in total, with a value of $2.60. What equation models the scenario?

a)

n + d = 32

.05n + .10d = 2.60

b)

n + d = 2.60

.05n + .10d = 32

c)

n + d = 32

.10n + .25d = 2.60

d)

n + d = 2.60

.10n + .25d = 32

13.

A piggy bank has dimes and quarters. The piggy bank has 25 coins, and has a value of $4.90. What system of equations models this scenario?

a)

d + q = 25

.10d + .25q = 4.90

b)

d + q = 4.90

.10d + .25q = 25

c)

d + q = 25

.05d + .10q = 4.90

d)

d + q = 4.90

.05d + .10q = 25

14.

You sell 15 rolls of wrapping paper for a fundraiser.  Shiny wrapping paper costs $4 and regular wrapping paper costs $2. The total for the 15 rolls was $44.  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
15.
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
16.
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
17.
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
18.
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? 
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
19.

Little Timmy has saved coins in his piggy bank. He has 40 dimes and nickels worth $3.35.

a)

n+d=3.35

0.05n+0.10d=40

b)

n+d=40

0.05n+0.10d=3.35

c)

n+d=40

5n+10d=3.35

d)

n+d=40

0.10n+0.05d=3.35

20.

Dominic is selling cookies for $1 and cupcakes for $5 to raise money for the basketball game. He raised a total of $532 from selling 248 deserts. Write a system to determine how many cookies, x, and cupcakes, y, he sold

a)

x+y=532

x+5y=248

b)

x+y=248

5x+y=532

c)

x+y=532

5x+y=248

d)

x+y=248

x+5y=532