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System of Equations Word Problems Slope Intercept Form

Total questions: 15

Worksheet time: 15mins

Name
Class
Date
1.

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?

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

2.

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?

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

3.

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.

a)

Adult $13
Child $5

b)

Adult $10
Child $6

c)

Adult $8
Child $16

d)

Adult $12
Child $13

4.

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

5.

What will the grade be after 3 hours?

a)

130

b)

43

c)

50

d)

70

6.

In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.

a)

y=5x−20y=5x-20

b)

y=20x+5y=20x+5

c)

y=5x+20y=5x+20

d)

y=20x−5y=20x-5

7.

What is the solutions to the following system of equations?

a)

(5,2)

b)

(2, 5)

c)

(0,3)

d)

Infinitely Many Solutions

e)

No Solutions

8.

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? 

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

9.

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

10.

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

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

11.

Cullin needs to save at least $100 for homecoming.  He works 2 jobs earning $8/hour at Culvers and $25/hour mowing lawns.  He only has time to work 14 hours before homecoming. 

a)

x + y  ≥ 25
x + y ≤ 8

b)

100x + 25 y ≤ 100
2x + 8y ≤ 14

c)

x + y ≥ 100
8x + 25y ≤ 14

d)

8x + 25y ≥ 100
x + y ≤ 14

12.

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

a)

b + t < 15
3b + 6t > 66

b)

b + t > 15
3b + 6t < 66

c)

3b + 6t > 15
b + t < 66

d)

3b + 6t < 15
b + t < 66

13.

Which shows the correct substitution?

a)

6x + 10 = 3x + 1

b)

6x + 10 = 6x + 10

14.

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?

a)

1.5x + 0.5y = 78.5

x + y = 87

b)

1.5x + 0.5y = 78.5

1.5x + 0.5y = 87

c)

x+ y = 78.5

1.5x + 0.5y = 87

d)

x + y = 78.5

x + y = 87

15.

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?

a)

1.5x+0.5y=78.5
x+y=87

b)

1.5x+0.5y=78.5
1.5x+0.5y=87

c)

x+y=78.5
1.5x+0.5y=87

d)

x+y=78.5
x+y=87