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01 Simple Linear Inequalities in One Variable Word Problems

Total questions: 20

Worksheet time: 5hrs 0mins

Name
Class
Date
1.
Which inequality is represented by the words " no more than" or "at most"?
a)
<
b)
>
c)
d)
2.
Which inequality is represented by the words " more than"?
a)
<
b)
>
c)
d)
3.
Which inequality is represented by the words " at least"?
a)
<
b)
>
c)
d)
4.

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

5.

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?

a)

1.75 + 0.65m < 10

b)

1.75 + 0.65m > 10

c)

1.75m + 0.65 < 10

d)

1.75m + 0.65 > 10

6.

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?

a)

6x + 8 ≥ 42

b)

8x + 6 ≤ 42

c)

6x + 8 > 42

d)

8x + 6 < 42

7.

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?

a)

25 - 12x ≥ 200

b)

25 + 12x ≥ 200

c)

13x ≥ 200

d)

25 + 12x < 200

8.

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?

a)

0.85x + 375 > 450

b)

0.85x + 375 < 450

c)

0.85 + 375x > 450

d)

0.85 + 375x < 450

9.

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

10.

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?

a)

125x + 55 < 600

b)

125x - 55 > 600

c)

125x + 55 > 600

d)

125x - 55 < 600

11.

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.

a)

4

b)

5

c)

6

d)

3

12.

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?

a)

15x + 2.5 < 10x + 3

b)

15 + 2.5x > 10 + 3x

c)

15 + 2.5x < 10 + 3x

d)

15 - 10 ≥ 2.5x + 3x

13.
The 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.
a)
80+9.50x > 120+7.50x
b)
80+9.50x < 120+7.50x
c)
80x+9.50 > 120x+7.50
d)
80x+9.50 < 120x+7.50
14.

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.

a)

50 + 20x < 18 + 30x

b)

50x + 20 < 18x + 30

c)

50 + 20x > 18 + 30x

d)

50x + 20 > 18x + 30

15.

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.

a)

3

b)

4

c)

5

d)

6

16.

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"?

a)

w4w\le4

b)

w8w\le8

c)

w4w\ge4

d)

w8w\ge8

17.

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=12bhA=\frac{1}{2}bh  }

a)

h18h\ge18

b)

h9h\ge9

c)

h4.5h\ge4.5

d)

h36h\ge36

18.

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!

a)

 m506m\le506  

b)

 m507m\le507  

c)

 m506m\ge506  

d)

 m507m\ge507  

19.

Review: When do we use the Flip Rule? Check all that apply.

a)

When we multiply by a negative

b)

When we divide by a negative

c)

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

d)

Whenever a negative appears in a problem

e)

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

20.

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.

a)

14

b)

15

c)

18

d)

19