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Linear Systems of Inequalities Word Problems

Total questions: 20

Worksheet time: 20mins

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.

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

3.

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

4.

a)

(1,3)

b)

(2,1)

c)

(3,4)

d)

(6,2)

5.

Which of the following is a solution to the systems of inequalities?

a)

(0, 0)

b)

(-3, 0)

c)

(2, -5)

d)

(3, -1)

6.

Which of the following is a solution to the systems of inequalities?

a)

(0, -2)

b)

(-3, 0)

c)

(-3, 2)

d)

(1, 1)

7.

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

8.

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

9.

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

a)

10x + 1.50 ≥ 40

b)

1.50x + 10 ≤ 40

c)

1.50x + 10 <40

d)

10x + 1.50 < 40

10.

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

a)

125x + 55 ≤ 600

b)

125x + 55 ≥ 600

c)

125x + 55 > 600

d)

125x + 55 < 600

11.

Mona is ordering cups for her school.  Company A charges $3.50 for each cup and a one-time starter fee of $14.  Company B charges $0.50 for each trophy and a one-time starter fee of $22.  
Which inequality can be used to find x, the minimum number of cups that can be ordereed so that the total charge at Company A is less than the total charge at Company B?

a)

3.5x + 14 < 0.5x + 22

b)

3.5x + 14 > 0.5x + 22

c)

3.5 + 14x < 0.5 + 22x

d)

3.5 + 14x > 0.5 + 22x

12.

Ross and Chandler go to Taco Land and order sodas for a total of $3.50. They also want to order some tacos (of course), which cost $1.75 each. If they have $20, how many tacos can they buy? Which inequality best represents the situation.

a)

3.50 + 1.75t > 20

b)

1.75 + 3.50t ≤ 20

c)

3.50 + 1.75t ≥ 20

d)

1.75t + 3.50 ≤ 20

13.

A willow tree is 5.1 feet tall and grows at a rate of 2.5 feet a year. After how many years will the tree have reached no more than 60 feet tall?

a)

5.1 + 2.5y ≥ 60

b)

60 < 5.1 + 2.5

c)

5.1 + 2.5y ≤ 60

d)

5.1 + 2.5y > 60

14.

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

a)

5x + 10 ≥ 100

b)

5x - 100 ≥ 10

c)

10x + 5 ≤ 100

d)

5x + 10 > 100

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 one of these is a valid solution?

a)

(3, 2)

b)

(1, 4)

c)

(2, 8)

d)

(5, 1)

16.

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

17.

Colin needs to save at least $200 for homecoming. He works 2 jobs earning $9/hour at Wawa and $25/hour mowing lawns. He only has time to work 16 hours before homecoming.

a)

x + y ≥ 25

x + y ≤ 9

b)

100x + 25 y ≤ 200

2x + 9y ≤ 16

c)

x + y ≥ 200

9x + 25y ≤ 16

d)

9x + 25y ≥ 200

x + y ≤ 16

18.

Which points are solutions for the system graphed:

a)

(-3, -10)

b)

(1, 6)

c)

(3, -7)

d)

(-1, -8)

e)

(-2, -6)

19.

A deli sells ham subs (h) for $6 each and meatball subs (m) for $8 each. The deli sells less than 40 subs on Monday. The total amount for all sales is less than $200. Which system of inequalities models this situation?

a)

h + m < 40h\ +\ m\ <\ 40
6h + 8m < 2006h\ +\ 8m\ <\ 200

b)

h + m > 40h\ +\ m\ >\ 40
6h + 8m > 2006h\ +\ 8m\ >\ 200

c)

h + m  40h\ +\ m\ \le\ 40
6h + 8m < 2006h\ +\ 8m\ <\ 200

d)

h + m 40h\ +\ m\ \le40
6h + 8m  2006h\ +\ 8m\ \le\ 200

20.

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