AlgebraVery hardInequality with two costs
Algebra practice question
A car rental costs $30 per day plus $0.20 per mile driven. A customer rents the car for 2 days and can spend at most $100 in total. What is the greatest number of miles the customer can drive?
Answer: 200
Two days cost 2(30) = 60 dollars, leaving 100 − 60 = 40 dollars for mileage. At 0.20 per mile: 0.2m ≤ 40, so m ≤ 200. Check: 60 + 0.2(200) = 100 exactly.
Common wrong answers
- If you answered 40
- 40 is the number of dollars left for mileage, not the number of miles. Divide by the 0.20 per-mile rate.
- If you answered 350
- 350 is (100 − 30)/0.2 — only ONE day's charge was subtracted. The rental is for two days, 60 dollars.
- If you answered 500
- 500 is 100/0.2, ignoring the daily charge altogether. The 60 dollars for two days must come out of the budget first.
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