Ratios, Rates, Proportional Relationships, and Units Flashcards

A painting crew can paint a house in 6 days working 8 hours a day. How many days would it take if they worked 12 hours a day instead?

Answer: 4

Total hours = 6 × 8 = 48; at 12 hr/day: 48 ÷ 12 = 4 days.

Oil and vinegar are mixed in a ratio of 2:5 in a salad dressing. If the total volume is 280 mL, how many mL of oil are in the dressing?

Answer: 80 mL

Oil fraction = 2/7; oil = (2/7) × 280 = 80 mL.

A car's fuel efficiency is 32 miles per gallon. If gas costs $3.60 per gallon, what is the fuel cost for a 400-mile trip?

Answer: $45.00

Gallons needed = 400 ÷ 32 = 12.5; cost = 12.5 × $3.60 = $45.00.

The ratio of red marbles to blue marbles is 3:2. If 5 red marbles are added, the ratio becomes 2:1. How many blue marbles are there?

Answer: 10

Let red = 3x and blue = 2x; (3x+5)/(2x) = 2 → 3x+5 = 4x → x = 5; blue = 2×5 = 10.

If 1 foot = 30.48 cm, what is 5 yards in centimeters? (1 yard = 3 feet)

Answer: 457.2 cm

5 yards = 15 feet = 15 × 30.48 = 457.2 cm.

A 500 mL bottle of juice is 30% real juice. A 1,000 mL bottle is 45% real juice. What percent of the combined mixture is real juice?

Answer: 40%

Real juice = 0.30×500 + 0.45×1,000 = 150 + 450 = 600 mL in 1,500 mL total; 600/1,500 = 40%.

A 60-liter solution is 35% alcohol. How many liters of pure alcohol must be added to make a 50% alcohol solution?

Answer: 18 L

Current alcohol = 0.35 × 60 = 21 L; let x = liters added: (21+x)/(60+x) = 0.50 → 21+x = 30+0.5x → 0.5x = 9 → x = 18.