Ratio and Proportion Flashcards

If mixing a solution requires a 3:1 ratio of water to chemical concentrate, how many gallons of concentrate are needed for 12 gallons of total solution?

Answer: 3 gallons

In a 3:1 ratio the total is 4 parts, so concentrate is 1/4 of 12 gallons = 3 gallons.

A motor runs at 1,800 RPM and is connected by a belt to a pulley with a 3:1 drive ratio. What is the output RPM of the driven pulley?

Answer: 600 RPM

A 3:1 drive ratio means the driven pulley turns at 1,800 ÷ 3 = 600 RPM.

Two gears mesh together. The drive gear has 48 teeth and the driven gear has 16 teeth. If the drive gear rotates at 200 RPM, how fast does the driven gear rotate?

Answer: 600 RPM

The gear ratio is 48:16 = 3:1, so the smaller driven gear rotates at 200 × 3 = 600 RPM.

An electrician earns $28 per hour and works 8 hours per day. At the same daily rate, how much does he earn in 5 days?

Answer: $1,120

Daily earnings are $28 × 8 = $224, so for 5 days: $224 × 5 = $1,120.

If a 3/4-inch conduit can hold 12 wires, how many wires can a 1.5-inch conduit (twice the diameter) hold, assuming capacity scales with the square of the diameter?

Answer: 48

When diameter doubles, area quadruples (2² = 4), so capacity is 12 × 4 = 48 wires.

A job requires the ratio of material cost to labor cost to be 2:3. If the total budget is $5,000, how much is allocated for labor?

Answer: $3,000

Labor is 3 out of 5 total parts, so labor cost = (3/5) × $5,000 = $3,000.

If 6 workers complete a task in 8 days, how many days will it take 4 workers to complete the same task?

Answer: 12 days

Total work = 6 × 8 = 48 worker-days; with 4 workers: 48 ÷ 4 = 12 days.