Ratios, Rates, Proportional Relationships, and Units Flashcards

A store sells apples at a rate of 3 for $1.50. At this rate, what is the cost of 8 apples?

Answer: $4.00

Unit price = $1.50 ÷ 3 = $0.50 each; 8 × $0.50 = $4.00.

Two quantities x and y are proportional. When x = 4, y = 10. What is the value of y when x = 14?

Answer: 35

The constant of proportionality k = y/x = 10/4 = 2.5; when x = 14, y = 2.5 × 14 = 35.

A pump can fill a tank at a rate of 240 liters per minute. How many hours will it take to fill a 43,200-liter tank?

Answer: 3

Time = 43,200 ÷ 240 = 180 minutes = 3 hours.

On a blueprint, a room is drawn as 4 cm wide and 6 cm long. If the scale is 1 cm = 2.5 m, what is the actual area of the room in square meters?

Answer: 150 m²

Actual dimensions: 4 × 2.5 = 10 m wide and 6 × 2.5 = 15 m long; area = 10 × 15 = 150 m².

A car's speed is 60 miles per hour. Which of the following correctly converts this speed to feet per second? (1 mile = 5,280 feet; 1 hour = 3,600 seconds)

Answer: 88 ft/s

60 × 5,280 ÷ 3,600 = 316,800 ÷ 3,600 = 88 feet per second.

A mixture contains sand and gravel in a ratio of 5:3. If there are 40 kg of sand, how many kg of gravel are in the mixture?

Answer: 24

Gravel = (3/5) × 40 = 24 kg.

A printer prints 180 pages in 4 minutes. At this constant rate, how many pages will it print in 1 hour and 10 minutes?

Answer: 3,150

Rate = 45 pages/min; 1 hr 10 min = 70 min; 45 × 70 = 3,150 pages.