Ratios, Rates, Proportional Relationships, and Units Flashcards

A car travels 315 miles on 9 gallons of gas. At this rate, how many miles can the car travel on 15 gallons?

Answer: 525

The unit rate is 315 ÷ 9 = 35 miles per gallon; 35 × 15 = 525 miles.

A recipe calls for 3 cups of flour for every 2 cups of sugar. If a baker uses 15 cups of flour, how many cups of sugar are needed?

Answer: 10

The flour-to-sugar ratio is 3:2, so sugar = (2/3) × 15 = 10 cups.

A train travels at 90 kilometers per hour. How many meters does it travel in 40 seconds? (1 km = 1,000 m; 1 hour = 3,600 seconds)

Answer: 1,000 m

90 km/hr = 90,000 m / 3,600 s = 25 m/s; 25 × 40 = 1,000 m.

A map uses a scale of 1 inch = 25 miles. On the map, two cities are 3.6 inches apart. What is the actual distance, in miles, between the two cities?

Answer: 90

Actual distance = 3.6 × 25 = 90 miles.

A solution is 20% salt by weight. How many grams of salt are in 350 grams of the solution?

Answer: 70 g

0.20 × 350 = 70 grams of salt.

If 5 workers can complete a job in 12 days, how many days will it take 15 workers to complete the same job, assuming all workers work at the same rate?

Answer: 4

Total worker-days = 5 × 12 = 60; with 15 workers: 60 ÷ 15 = 4 days.

The density of a metal block is 8 grams per cubic centimeter. What is the volume, in cubic centimeters, of a block that has a mass of 520 grams?

Answer: 65

Volume = mass ÷ density = 520 ÷ 8 = 65 cm³.