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## Mathematics

## Mathematics

## 8th

## grade

# 01 Linear Inequalities in One Variable Word Problems

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8th

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Matthew Kilgore

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- 1. Multiple Choice15 minutes1 ptWhich inequality is represented by the words " no more than" or "at most"?<>≤≥
- 2. Multiple Choice15 minutes1 ptWhich inequality is represented by the words " more than"?<>≤≥
- 3. Multiple Choice15 minutes1 ptWhich inequality is represented by the words " at least"?<>≤≥
- 4. Multiple Choice15 minutes1 pt
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?

15h ≤ 105

15h > 105

15h < 105

15h ≥ 105

- 5. Multiple Choice15 minutes1 pt
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 a taxi ride.

Which inequality best describes how many miles Katie can ride in this taxi?

1.75 + 0.65m

__<__101.75 + 0.65m

__>__101.75m + 0.65

__<__101.75m + 0.65

__>__10 - 6. Multiple Choice15 minutes1 pt
The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Which inequality represents this scenario if “x” represents the number of games Cameron can play?

6x + 8 ≥ 42

8x + 6 ≤ 42

6x + 8 > 42

8x + 6 < 42

- 7. Multiple Choice15 minutes1 pt
Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks.

Which inequality could help you find how many dogs Katie would have to walk to reach her goal?

25 - 12x ≥ 200

25 + 12x ≥ 200

13x ≥ 200

25 + 12x < 200

- 8. Multiple Choice15 minutes1 pt
A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

0.85x + 375 > 450

0.85x + 375 < 450

0.85 + 375x > 450

0.85 + 375x < 450

- 9. Multiple Choice15 minutes1 pt
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?

5x + 10 ≥ 100

5x - 100 ≥ 10

10x + 5 ≤ 100

5x + 10 > 100

- 10. Multiple Choice15 minutes1 pt
The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour but offers a $55 discount for clients who pay ahead of time.

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 if the committee pays ahead of time?

125x + 55 < 600

125x - 55 > 600

125x + 55 > 600

125x - 55 < 600

- 11. Multiple Choice15 minutes1 pt
The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Use an inequality to determine the maximum number of games Cameron can play.

4

5

6

3

- 12. Multiple Choice15 minutes1 pt
The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride.

Which inequality could be used to determine how many rides you would need to go on before it would become cheaper to go to the Frederick fair?

15x + 2.5 < 10x + 3

15 + 2.5x > 10 + 3x

15 + 2.5x < 10 + 3x

15 - 10 ≥ 2.5x + 3x

- 13. Multiple Choice15 minutes1 ptThe Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge more than The Magic Carpet.80+9.50x > 120+7.50x80+9.50x < 120+7.50x80x+9.50 > 120x+7.5080x+9.50 < 120x+7.50
- 14. Multiple Choice15 minutes1 pt
Cody’s Gym charges a $18 fee to join and $30 per month. Tyler’s Gym charges a $50 fee to join and $20 per month. Write an inequality that could be used to determine how many months you will have to go to the gym before Tyler’s gym would be the better deal.

50 + 20x < 18 + 30x

50x + 20 < 18x + 30

50 + 20x > 18 + 30x

50x + 20 > 18x + 30

- 15. Multiple Choice15 minutes1 pt
Cody’s Gym charges a $18 fee to join and $30 per month. Tyler’s Gym charges a $50 fee to join and $20 per month.

Use an inequality to determine how many months will you have to go to the gym before Tyler’s gym becomes the better deal.

3

4

5

6

- 16. Multiple Choice15 minutes1 pt
A rectangle has a length that is seven inches longer than its width (w).

If the perimeter of this rectangle is at most 30 inches, which of the following inequalities gives the possible values of "w"?

$w\le4$

$w\le8$

$w\ge4$

$w\ge8$

- 17. Multiple Choice15 minutes1 pt
A triangular lot is known to have an area of at least 180 square meters. If the base of this lot is 20 meters, which of the following inequalities gives the possible values of the height?

{ Recall: $A=\frac{1}{2}bh$ }$h\ge18$

$h\ge9$

$h\ge4.5$

$h\ge36$

- 18. Multiple Choice15 minutes1 pt
The budget for a banquet is $1,900. If it costs $3.75 to serve a single meal at this banquet, which inequality describes the possible numbers of meals (m) that can be served?

Read each answer choice carefully!$m\le506$

$m\le507$

$m\ge506$

$m\ge507$

- 19. Multiple Choice15 minutes1 pt
Review: When do we use the Flip Rule? Check all that apply.

When we multiply by a negative

When we divide by a negative

When "x" ends up on the right-hand side

Whenever a negative appears in a problem

When "x" ends up on the left-hand side

- 20. Multiple Choice15 minutes1 pt
Katie wants to have at least $200 in her bank account by the end of the month. She currently has $25 in her bank account. Katie makes $12 for each dog that she walks.

Use an inequality to find how many dogs Katie must walk in order to meet her goal.

14

15

18

19

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