LEAP Ratios and Proportional Relationships 3 — Questions and Answers
Question 1: A table shows that y is proportional to x. When x = 4, y = 20. What is the constant of proportionality?
- 4
- 5 (Correct answer)
- 16
- 80
Correct answer: 5
The constant of proportionality k = y/x = 20/4 = 5.
Question 2: Which graph represents a proportional relationship?
- A curve passing through (0, 3)
- A straight line passing through the origin (Correct answer)
- A straight line with y-intercept at 2
- A horizontal line at y = 4
Correct answer: A straight line passing through the origin
A proportional relationship is represented by a straight line that passes through the origin (0, 0).
Question 3: At a bake sale, 4 cookies cost $2.00. Complete the table: how much do 10 cookies cost?
- $4.00
- $4.50
- $5.00 (Correct answer)
- $5.50
Correct answer: $5.00
Each cookie costs $2.00 ÷ 4 = $0.50, so 10 cookies cost 10 × $0.50 = $5.00.
Question 4: A proportion states: 6/x = 18/27. What is the value of x?
- 7
- 8
- 9 (Correct answer)
- 10
Correct answer: 9
Cross-multiplying gives 6 × 27 = 18x, so 162 = 18x, and x = 9.
Question 5: A 12-ounce juice bottle contains 42 calories. How many calories are in a 20-ounce bottle of the same juice?
- 60
- 65
- 70 (Correct answer)
- 75
Correct answer: 70
The unit rate is 42/12 = 3.5 calories per ounce; 20 × 3.5 = 70 calories.
Question 6: A scale model of a building is built at a ratio of 1:200. If the model is 15 cm tall, how tall is the actual building?
- 200 cm
- 1,500 cm
- 3,000 cm (Correct answer)
- 30,000 cm
Correct answer: 3,000 cm
Multiply the model height by the scale factor: 15 × 200 = 3,000 cm.
Question 7: A faucet leaks at a rate of 3 gallons every 4 hours. How many gallons will leak in 24 hours?
- 12 gallons
- 15 gallons
- 18 gallons (Correct answer)
- 21 gallons
Correct answer: 18 gallons
Set up the proportion 3/4 = x/24; cross-multiplying gives x = 72/4 = 18 gallons.
LEAP Ratios and Proportional Relationships 3
A table shows that y is proportional to x.
When x = 4, y = 20.
What is the constant of proportionality?