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System of Linear Inequalities Word Problems

Total questions: 20

Worksheet time: 20mins

Name
Class
Date
1.

Johnny earns $15 per hour dog walking. He wants to earn at least $105 to buy a new bike. Which inequality represents how long Johnny needs to work to afford his new bike?

a)

15h ≤ 105

b)

15h > 105

c)

15h < 105

d)

15h ≥ 105

2.

Gideon needs to collect at least 1,000 signatures for a petition to free all Koalas from zoos. He has 520 and wants to collect the same number each week. He has 6 more weeks. Which inequality represents this situation?

a)

520x+61000520x+6\le1000  

b)

520+6x1000520+6x\ge1000  

c)

520x+61000520x+6\ge1000  

d)

520+6x1000520+6x\le1000  

3.

Aidan wants to spend under $15 on lunch. He decides to buy pizza slices, which cost $2.50 each and a two liter soda which costs $1.75. Which inequality represents this situation?

a)

15>2.50x+1.7515>2.50x+1.75  

b)

152.50x+1.7515\le2.50x+1.75  

c)

152.50+1.75x15\ge2.50+1.75x  

d)

15<2.50+1.75x15<2.50+1.75x  

4.

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs $7 and a pizza costs $13. 

a)

7x + 13y < 81

b)

7x + 13y ≥ 81

c)

7x + 13y ≤ 81

d)

7x + 13y > 81

5.

a)

(1,3)

b)

(2,1)

c)

(3,4)

d)

(6,2)

6.

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

7.

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 \ge 2000

b)

x + y \le 300
7.5x + 5.5y \ge 2000

c)

x + y \le 300
7.5x + 5.5y \le 2000

d)

x + y >> 2000
7.5x + 5.5y \le 300

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.

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

a)

(0, 0)

b)

(-3, 0)

c)

(2, -5)

d)

(3, -1)

10.

Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell?

a)

x/5.50 ≥ 5225

b)

5.50x ≥ 5225

c)

x + 5.50 ≤ 5225 

d)

x - 5.50 ≤ 5225

11.

Write the linear inequality in standard form for this situation: In order to raise money to attend upcoming competitions, the Math Pentathalon team is selling apple cider and hot chocolate. They hope to make at least $240 by selling hot chocolate for $1 a glass and hot apple cider for $2 a glass.

a)

x + 2y < 240

b)

x + 2y > 240

c)

x + 2y ≤ 240

d)

x + 2y ≥ 240

12.

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

13.

Your family goes to a restaurant for dinner. There are people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill 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

14.

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

15.

Jasmine is helping her mom with a small vegetable patch. Tomato plants are selling for $4, and pepper plants are selling for $3. They don't want to spend more than $60. Which combination of tomato plants and pepper plants will they be able to purchase?

a)

10 tomato plants and 9 pepper plants

b)

5 tomato plants and 15 pepper plants

c)

12 tomato plants and 6 pepper plants

d)

6 tomato plants and 11 pepper plants

16.

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

17.

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

3.5x+5y803.5x+5y\ge80

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

18.

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

19.

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

20.

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