Problem 5 · 2014 AMC 8
Easy
Ratios, Rates & Proportions
unit-rate
Margie's car can go 32 miles on a gallon of gas, and gas currently costs $4 per gallon. How many miles can Margie drive on $20 worth of gas?
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Answer: C — 160 miles.
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Hint 1 of 2
Chain the units: dollars → gallons → miles. Each arrow is one given rate, so you never have to guess what to multiply.
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Hint 2 of 2
Dollars to gallons uses $4/gallon; gallons to miles uses 32 miles/gallon.
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Approach: chain the rates: dollars → gallons → miles
- Dollars → gallons: 20 ÷ 4 = 5 gallons.
- Gallons → miles: 5 × 32 = 160 miles.
- Reusable trick: line up the units so the ones you don't want cancel ($ × gal/$ × mi/gal leaves just miles). Then the arithmetic takes care of itself.
Another way — miles per dollar in one step:
- Each dollar buys 32 ÷ 4 = 8 miles of driving.
- $20 × 8 miles/$ = 160 miles.
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