Exploring Proportional Relationships and Equations

1. Sarah has 3 times as many apples as Tom. If Tom has x apples, write an equation to represent the number of apples Sarah has. How many apples do they have together if Tom has 4 apples?

• 8 apples

• 20 apples

• 16 apples

• 12 apples

2. A car travels at a constant speed of 60 miles per hour. Write an equation to represent the distance (d) traveled after t hours. How far will the car travel in 3 hours?

• 120 miles

• 240 miles

• 150 miles

• 180 miles

3. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to make a batch with 9 cups of sugar, how many cups of flour do you need? Write an equation to represent this relationship.

• 6 cups of flour

• 8 cups of flour

• 4 cups of flour

• 10 cups of flour

4. The cost of 5 notebooks is $10. Write an equation to find the cost (C) of n notebooks. How much would 8 notebooks cost?

• $8

• $12

• $20

• $16

5. A gardener plants 4 rows of flowers, with each row containing x flowers. Write an equation to represent the total number of flowers. If there are 6 flowers in each row, how many flowers are there in total?

• 18

• 24

• 20

• 30

6. A store sells pencils for $0.50 each. Write an equation to find the total cost (C) for buying p pencils. How much would it cost to buy 10 pencils?

• $5.00

• $10.00

• $3.00

• $7.50

7. A bike rental shop charges a flat fee of $15 plus $5 for each hour rented. Write an equation to represent the total cost (C) for h hours. How much would it cost to rent a bike for 4 hours?

• $35

• $50

• $45

• $25

8. If a train travels 80 miles in 2 hours, write an equation to find the speed (s) of the train in miles per hour. What is the speed of the train?

• 40 miles per hour

• 30 miles per hour

• 60 miles per hour

• 50 miles per hour

9. A school is planning a field trip and needs to rent buses. Each bus can hold 20 students. Write an equation to find the number of buses (b) needed for s students. How many buses are needed for 75 students?

• 5

• 6

• 4

• 3

10. A recipe requires 3 cups of water for every 2 cups of rice. If you want to cook 6 cups of rice, how many cups of water do you need? Write an equation to represent this relationship.

• 9 cups of water

• 12 cups of water

• 3 cups of water

• 6 cups of water