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Systems of Equations Word Problems

Total questions: 15

Worksheet time: 2hrs 45mins

Name
Class
Date
1.

The school that Mark goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 6 adult tickets and 2 student tickets for a total of $90. The school took in $132 on the second day by selling 8 adult tickets and 4 student tickets. What is the price each of one adult ticket and one student ticket?

a)

adult ticket: $12, student ticket: $9

b)

adult ticket: $9, student ticket: $12

c)

adult ticket: $18, student ticket: $12

d)

adult ticket: $15, student ticket: $8

2.

Stefan and Jack are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Stefan sold 7 rolls of plain wrapping paper and 4 rolls of holiday wrapping paper for a total of $152. Jack sold 5 rolls of plain wrapping paper and 8 rolls of holiday wrapping paper for a total of $196. What is the cost each of one roll of plain wrapping paper and one roll of holiday wrapping paper?

a)

roll of plain wrapping paper: $12, roll of holiday wrapping paper: $17

b)

roll of plain wrapping paper: $16, roll of holiday wrapping paper: $19

c)

roll of plain wrapping paper: $17, roll of holiday wrapping paper: $12

d)

roll of plain wrapping paper: $8, roll of holiday wrapping paper: $18

3.

Shreya and Micaela are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and packages of crocus bulbs. Shreya sold 8 bags of windflower bulbs and 5 packages of crocus bulbs for a total of $70. Micaela sold 4 bags of windflower bulbs and 4 packages of crocus bulbs for a total of $44. Find the cost each of one bag of windflower bulbs and one package of crocus bulbs.

a)

bag of windflower bulbs: $6, package of crocus bulbs: $2

b)

bag of windflower bulbs: $6, package of crocus bulbs: $3

c)

bag of windflower bulbs: $5, package of crocus bulbs: $6

d)

bag of windflower bulbs: $3, package of crocus bulbs: $9

4.

Jill and Ashley are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Jill sold 2 small boxes of tangerines and 8 large boxes of tangerines for a total of $182. Ashley sold 3 small boxes of tangerines and 4 large boxes of tangerines for a total of $121. Find the cost each of one small box of tangerines and one large box of tangerines.

a)

small box of tangerines: $7, large box of tangerines: $14

b)

small box of tangerines: $15, large box of tangerines: $19

c)

small box of tangerines: $8, large box of tangerines: $17

d)

small box of tangerines: $6, large box of tangerines: $13

5.

The senior classes at High School A and High School B planned separate trips to the state fair. The senior class at High School A rented and filled 3 vans and 3 buses with 210 students. High School B rented and filled 6 vans and 2 buses with 188 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

a)

Van: 19, Bus: 37

b)

Van: 6, Bus: 64

c)

Van: 14, Bus: 50

d)

Van: 12, Bus: 58

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.

Last season two running backs on the Steelers football team rushed for a combined total of 1550 yards.  One rushed for 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
8.
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
9.
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
10.
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? 
a)
y = 9.65 + x
y = 8.40 + x
b)
y = 9.65x + 43
y = 8.40x + 58
c)
y =9.65x
y = 8.40x
d)
y = 9.65x - 43
y = 8.40x - 58
11.

Which graph represents the equation y=4x1y=4x-1  

a)
b)
c)
d)
12.
Which equation represents the following graph?
a)
y = 3x + 2
b)
y = -2x + 3
c)
y = 2x + 3
d)
y = -3x + 2
13.
Give the equation for the graph
a)
y = 5x - 3
b)
y = 4x + 2
c)
y =-2x + 5
d)
y = - 2x + 4
14.
Graph. y = 2/3x - 3
a)
a
b)
b
c)
c
d)
d
15.
Graph. y = -4
a)
a
b)
b
c)
c
d)
d