Free Printable 10/27 Equations & Inequalities Word Problems

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10/27 Equations & Inequalities Word Problems

Total questions: 40

Worksheet time: 7hrs 31mins

Name

Class

Date

Carol wants to join a dance studio. Studio A charges $100.00 for the entry fee and $45.00 per class, while Studio B charges $125.00 for the entry fee and $30.00 per class. Write an equation to determine how many classes would need to be taken for the price to be equal?

125 - 100 = 45x + 30x

100x + 45 = 125x + 30

100 + 45x = 125 + 30x

100 - 45x = 125 - 30x

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. Which equation could be used to determine how many miles would have to be driven in one day for both rental agencies to cost the same amount to rent?

30 + 0.15x = 36 + 0.10x

30 - 0.15x = 36 - 0.10x

30 + 36 = 0.10x + 0.36x

36 - 30 = 0.36x + 0.10x

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

150x + 24 = 180 + 20x

150 + 24x = 180 + 20x

180 - 150 = 24 x + 20x

150 - 24x = 180 - 20x

Write an inequality to represent the following relationship:
Three times a number minus two is less than the number plus ten.

3x - 2 < x + 10

2 - 3x < x + 10

3x - 2 > x + 10

2 - 3x > x + 10

Select the situation that could be modeled by: 2x + 4 = 3x

The number of students in the 2-year-old class and the 4-year-old class equals the number of students in the 3-year-old class. How many students are in each class?

Cade bought 2 books for $4 each and Clara bought 3 books. How much did Clara pay?

Dean is 4 more than twice his brother’s age. He is also 3 times his brother’s age. How old is Dean’s brother?

Select the situation that could be modeled by: 12 + 5x = 18+3x

Derek charges a base fee of $12 to walk a dog plus $5 per hour. Darla charges a base fee of $18 plus $3 an hour to walk a dog. After how many hours would they make the same amount of money?

Andy buys 12 sodas for $5 each. Alex buys 18 sodas for $3 each. If they each spent the same amount, how much did they spend?

Brian charges $12 for a hat and $5 per shirt. Blake buys 3 hats and 18 shirts. How many hats and shirts must they sell to make the same amount of money?

Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tyler’s gym would be a better deal.

30 + 20x < 15 + 30x

30x + 20 < 15x + 30

30 + 20x > 15 + 30x

30x + 20 > 15x + 30

10x + 9 = 4x - 9

-3

-18

2(x + 6) + 3 = 9 + 5x

-8

-10

10.

-6(1 - 6r) = -2(r + 3)

all real numbers

no solution

11.

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

2 hours

3 hours

4 hours

5 hours

12.

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

3 hours

4 hours

1 hour

2 hours

13.

Joaquin has a $50 gift card from Pizza Palace. All pizzas at Pizza Palace cost $7 each. Joaquin wants to give the driver a $5 tip for delivering the pizza. Which inequality could be used to determine the possible number of pizzas, p, he could order with his gift card, including the tip?

7p + 5 ≤ 50

(7 + 5)p ≤50

7p + 5 ≥ 50

7p + 5 < 50

14.

2(2x + 4) > 20

Not Shown

15.

- (8n - 2) = 3 + 10(1 - 3n)

n = 1/2

n = -1/2

n = 2

16.

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 equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

17.

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?

3.5x + 14 < 0.5x + 22

3.5x + 14 > 0.5x + 22

3.5 + 14x < 0.5 + 22x

3.5 + 14x > 0.5 + 22x

18.

What is the first step you should take to solve this equation:

3\left(x-2\right)=2x+7

Add 2 to both sides

Use distributive property to get rid of the parentheses

Isolate the variable on one side

Subtract 7 from both sides

19.

Check all steps that you would need to take to solve this equation:

8\left(2x-3\right)+2x=4x-4

Use distributive property to get rid of parentheses

Combine like terms

Move the variable to one side of the equation

Use inverse operations to isolate and solve for the variable.

20.

Check all that apply - What could you do to move the variable to one side of this equation:
$2x+3=4x-7$

Subtract 2x from both sides

Subtract 3 from both sides

Subtract 4x from both sides

Add 7 to both sides

21.

Jacob solved the following equation using the steps shown.

Step 1 5x + 9 = 2x - 3

Step 2 3x + 9 = -3

Step 3 3x = -12

Step 4 x = -4

What operation did he perform to get from Step 1 to Step 2?

Subtracted 2x from both sides of the equation

Subtracted 9 from both sides of the equation

Multiplied both sides of the equation by 3

Added -3 to both sides of the equation

22.

What would be the best next step in solving this equation:

1+4n=10-14n

Subtract 14n from both sides

Add 14n to both sides

Add 10 to both sides

23.

Solve:

2x-5=3x+4

Enter only the value of x, not "x = (a) ". No spaces.

24.

Solve:

5w+5=8w-10

-5

-2

25.

Solve for x:
4(1-x)+3x=-2(x+1)

x = -6

x = 6

x = 3

26.

Solve:
2(4x-3) - 8 = 4 + 2x

x = 5/3

x = 3

x = 1

x = 2

27.

Solve the equation
12x - 15 = 3(2x+3)

x = 4

x = -4

x = 2

x = -2

28.

Solve the equation
-8x - 8 +3(x - 2) = -3x + 2

x = -8

x = 8

x = 2

x = -2

29.

Which of the following scenarios could be used to represent the inequality shown in the image?

The student council is ordering T-shirts from a website. The T-shirts cost $9 each and there is a shipping fee of $8 for any amount ordered. The student council wants to spend no more than $80 on the T-shirts. What are the possible number of T-shirts they can order?

The student council is ordering T-shirts from a website. The T-shirts cost $9 each and there is a shipping fee of $8 for any amount ordered. The student council wants to spend more than $80 on the T-shirts. What are the possible number of T-shirts they can order?

The student council is ordering T-shirts from a website. The T-shirts cost $9 each and there is a shipping fee of $8 for any amount ordered. The student council wants to spend less than $80 on the T-shirts. What are the possible number of T-shirts they can order?

The student council is ordering T-shirts from a website. The T-shirts cost $9 each and there is a shipping fee of $8 for any amount ordered. The student council wants to spend exactly $80 on the T-shirts. What are the possible number of T-shirts they can order?

30.

Which situation can be represented by the equation
100 – 2x = 140 – 6x?

Tank A has 100 gallons of water and gains 2 gallons per hour. Tank B has 140 gallons and gains 6 gallons per hour. When will the tanks have the same amount of water?

Tank A has 100 gallons of water and loses 2 gallons per hour. Tank B has 140 gallons and loses 6 gallons per hour. When will the tanks have the same amount of water?

Tank A has 100 gallons of water and gains 2 gallons per hour. Tank B has 140 gallons and gains 6 gallons per hour. When will Tank A have more water than Tank B?

Tank A has 100 gallons of water and loses 2 gallons per hour. Tank B has 140 gallons and loses 6 gallons per hour. When will Tank A have more water than Tank B?

31.

What is the solution to the inequality $5y - 7 \ge 5y - 3$ ?

No solution.

y > 2

y < 2

y = 2

32.

Solve:

5x + 4 = 5x − 3

x = 4

x = -3

infinitely many solutions

no solutions

33.

Solve:

2y − 3 = 2y − 3

y = 0

y = -3

infinitely many solutions

no solutions

34.

Solve:

3(x − 2) = 3x − 6

x = 6

x = -6

infinitely many solutions

no solutions

35.

SOLVE THE INEQUALITY:

$3x-1<2x+4+x$

x < 5

x < 3

No Solution

All Real Numbers

36.

SOLVE THE INEQUALITY:

$x+2x+1>5+3x$

x < -4

x > 4

No Solution

All Real Numbers

37.

SOLVE THE INEQUALITY:

$-2\left(x+3\right)\ge-2x-6$

x $\ge$ 0

x $\le$ 0

No Solution

All Real Numbers

38.

Solve the inequality:

-2(5 + 6n) < 6(8 − 2n)

No Solution

All Real Numbers

x < 0

x > 0

39.

Solve the inequality:

4(2x - 1) > 2(3x + 1) + 2x

x > 6

All Real Numbers

x > 3

No Solution

40.

Solve.

a > -24

a > 6

a > -36

a > -10

Reset

10/27 Equations & Inequalities Word Problems

Total questions: 40

Worksheet time: 7hrs 31mins

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