2020 AMC 12A Problem 3

Attempt Problem 3 of the 2020 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

3.

A driver travels for 22 hours at 6060 miles per hour, during which her car gets 3030 miles per gallon of gasoline. She is paid $0.50\$0.50 per mile, and her only expense is gasoline at $2.00\$2.00 per gallon. What is her net rate of pay, in dollars per hour, after this expense?
2020
2222
2424
2525
2626
Answer: E
Concepts:rateunit conversion
Small hint:
In 22 hours she drives 120120 miles; find her pay and her gasoline cost for that distance
Big hint:
Divide the net earnings by the 22 hours to get the rate per hour
Solution:
In 22 hours she drives 120120 miles, earning 120⋅$0.50=$60.120 \cdot \$0.50 = \$60.
She uses 120÷30=4120 \div 30 = 4 gallons, costing 4⋅$2.00=$8.4 \cdot \$2.00 = \$8.
Her net earnings are $60−$8=$52,\$60 - \$8 = \$52, so her rate is $52÷2=$26\$52 \div 2 = \$26 per hour.
Thus, E is the correct answer.
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