Equations & Inequalities: Real-World Problem Solving

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an equation to represent the number of apples Sarah has. If together they have 30 apples, how many apples does each have?

• Tom has 10 apples and Sarah has 20 apples.

• Tom has 12 apples and Sarah has 24 apples.

• Tom has 5 apples and Sarah has 15 apples.

• Tom has 8 apples and Sarah has 16 apples.

2. A store sells pencils for $0.50 each and erasers for $0.75 each. If the total cost of x pencils and y erasers is $10, write an equation to represent this situation. If x = 10, how many erasers can be bought?

• 4

• 8

• 6

• 10

3. A rectangle's length is 3 meters more than its width. If the perimeter of the rectangle is 30 meters, write an equation to find the width. What is the width and length of the rectangle?

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

• Width: 4 meters, Length: 7 meters

4. The sum of three consecutive integers is 72. Write an equation to find the integers. What are the three integers?

• 25, 26, 27

• 21, 22, 23

• 20, 21, 22

• 23, 24, 25

5. A car rental company charges a flat fee of $20 plus $0.15 per mile driven. If a customer paid $50, write an equation to find the number of miles driven. How many miles did the customer drive?

• 100 miles

• 150 miles

• 250 miles

• 200 miles

6. A school is selling tickets for a play. Adult tickets cost $8 and student tickets cost $5. If the total revenue from selling x adult tickets and y student tickets is $200, write an equation to represent this. If 10 adult tickets were sold, how many student tickets were sold?

• 24

• 20

• 30

• 18

7. A gardener has 50 feet of fencing to create a rectangular garden. If the length is 5 feet more than the width, write an equation to find the dimensions of the garden. What are the length and width?

• Width: 10 feet, Length: 15 feet

• Width: 8 feet, Length: 13 feet

• Width: 12 feet, Length: 17 feet

• Width: 5 feet, Length: 10 feet

8. A movie theater has a total of 200 seats. If the number of adult tickets sold is 20 more than the number of child tickets sold, write an equation to represent this situation. How many adult and child tickets were sold?

• Adult tickets: 100, Child tickets: 100

• Adult tickets: 120, Child tickets: 80

• Adult tickets: 90, Child tickets: 110

• Adult tickets: 110, Child tickets: 90

9. A bike costs $150 and a helmet costs $30. If a customer buys x bikes and y helmets for a total of $600, write an equation to represent this. If 2 bikes were purchased, how many helmets can be bought?

• 8 helmets

• 5 helmets

• 15 helmets

• 10

10. A student scored 75% on a test with 40 questions. If the student answered x questions correctly, write an equation to find x. How many questions did the student answer correctly?

• 30

• 35

• 40

• 25