Ratios, Rates, Proportional Relationships, and Units Flashcards

A store increases the price of a shirt from $40 to $52. What is the percent increase?

Answer: 30%

Percent increase = (52 − 40)/40 × 100 = 12/40 × 100 = 30%.

Kira can read 40 pages in 50 minutes. At this rate, how many pages can she read in 2 hours 15 minutes?

Answer: 108 pages

Rate = 40/50 = 4/5 pages per minute; 2 hr 15 min = 135 minutes; pages = 135 × 4/5 = 108.

A road map has a scale of 1 in : 40 miles. Two cities are 3.25 inches apart on the map. What is the actual distance?

Answer: 130 miles

Actual distance = 3.25 × 40 = 130 miles.

A bank offers 5% annual simple interest. How much interest does $4,000 earn over 30 months?

Answer: $500

30 months = 2.5 years; I = 4,000 × 0.05 × 2.5 = $500.

At a factory, 3 machines produce 720 parts per hour. How many parts do 7 machines of the same type produce in 2.5 hours?

Answer: 4,200 parts

Rate per machine = 720 ÷ 3 = 240 parts/hr; 7 machines × 240 × 2.5 = 4,200 parts.

A recipe for 4 servings requires 1.5 cups of oats. How many cups of oats are needed for 10 servings?

Answer: 3.75 cups

Per serving = 1.5 ÷ 4 = 0.375 cups; for 10 servings = 10 × 0.375 = 3.75 cups.

A rope is cut into four pieces whose lengths are in the ratio 1:2:3:4. The total length is 60 cm. What are the lengths of the two middle pieces?

Answer: 12 cm and 18 cm

Total parts = 1+2+3+4 = 10; one part = 60/10 = 6 cm; pieces are 6, 12, 18, 24 cm; middle two = 12 and 18 cm.