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Solving Systems of Inequalities Word Problems

Total questions: 15

Worksheet time: 15mins

Name
Class
Date
1.

Write the system of inequalities:
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

a)

x + y ≤ 300
7.5x + 5.5y ≥ 2000

b)

x + y < 300
7.5x + 5.5y ≥ 2000

c)

x + y ≤ 300
7.5x + 5.5y ≤ 2000

d)

x + y > 2000
7.5x + 5.5y ≤ 300

2.

Jonah is going to the store to buy candles. Small candles cost $3.50, and large candles cost $5.00. He needs to buy at least 20 candles and cannot spend more than $80. Write a system of linear inequalities that represents the situation.

a)

x+y20x+y\le20

b)

xy20xy\ge20
3.5+5y803.5+5y\le80

c)

xy20x-y\ge20
3.5x+5y803.5x+5y\le80

d)

x+y20x+y\ge20
3.5x+5y803.5x+5y\le80

3.

Gabriela is the manager of a print shop. She needs to schedule employees to work no more than 300 person-hours per week. She has one 20 hour a week part-time employee. Each full-time employee works 40 hours per week. Which inequality will determine f, the number of full-time employees Gabriela can schedule to remain under the 300 person-hour per week limit?

a)

20 + 40f  30020\ +\ 40f\ \le\ 300

b)

40 + 20f  30040\ +\ 20f\ \ge\ 300

c)

20 + 40f  30020\ +\ 40f\ \ge\ 300

d)

20f + 40 < 30020f\ +\ 40\ <\ 300

4.

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

5.

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

6.

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

a)

x+y≤300
7.5x+5.5y≥2000

b)

x+y<300
7.5x+5.5y≥2000

c)

x+y≤300
7.5x+5.5y≤2000

d)

x+y>2000
7.5x+5.5y≤300

7.

Write the system of inequalities
Eiko is drawing caricatures at a fair for 8 hours (480 minutes). She can complete a small drawing in 15 minutes and charges $10 for the drawing. She can complete a larger drawing in 45 minutes and charges $25 for the drawing. Eiko hopes to make at least $200 at the fair. 

a)

10x+15y≤480
45x+25y≥250

b)

10x+25y≤200
15x+45y≤480

c)

10x+25y>200
15x+45y<480

d)

10x+25y≥200
15x+45y≤480

8.

Christian had brochures printed for a new business venture. Christian originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which is at least a total of $134. After those ran out, Christian spent at most $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

a)

x+y>or=134
x+y > or =120

b)

3x+3y < or=134
4x+3y < or =120

c)

4x+3y > or =134
3x+3y < or = 120

d)

7xy=134
6xy > 120

9.

Write the system of inequalities Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing. Which is a possible solution?

a)

300 adults and 0 children

b)

200 adults and 1 children

c)

100 adults and 100 children

d)

300 adults and 100 children

10.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

11.

What is the title of topic 5 for Unit 3 ?

a)

3 method review

b)

Solving Systems of Inequalities

c)

Conceptual Understanding

d)

Function Notation

12.

Cole is doing a basketball challenge for charity. In order to win money for the charity, he needs to score at least 20 points in less than 10 shots. If x is the number of 2-point shots, and y is the number of three point shots, which inequalities below represent the situation?

a)

x + y < 10

2x + 3y ≥ 20

b)

x + y ≤ 10

2x + 3y ≥ 20

c)

x + y ≤ 10

2x + 3y > 20

d)

x + y < 10

2x + 3y > 20

13.

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

a)

1.75 + 0.65m < 10

b)

1.75 + 0.65m > 10

c)

1.75m + 0.65 < 10

d)

1.75m + 0.65 > 10

14.

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

a)

2x + 3y > 100

x + y ≤ 40

b)

100x + 2y > 3

x + y ≤ 40

c)

100x + 40y > 100

3x + 2y ≤ 40

d)

3x + 2y > 100

x + y ≤ 40

15.

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?

a)

x + y ≥ 6
32x + 20y ≤ 150

b)

x + y ≥ 632
x + 20y ≥ 150

c)

x + y ≤ 6
32x + 20y ≤ 150

d)

x + y ≤ 6
32x + 20y ≥ 150