How many miles did she drive?

Question

A car rental company offers two plans. The Standard plan costs $34 per day plus $0.20 per mile driven. The Premium plan costs $66 per day plus $0.12 per mile driven. A customer rents a car for 3 days and finds that the two plans would cost the same total amount for the number of miles she drove.

Accepted Answer

D. 1,200. For m miles over 3 days, the Standard plan costs 3(34) + 0.20m = 102 + 0.20m and the Premium plan costs 3(66) + 0.12m = 198 + 0.12m. Setting these equal: 102 + 0.20m = 198 + 0.12m, so 0.08m = 96 and m = 1,200. Check: 102 + 240 = 342 and 198 + 144 = 342. Choice C encodes using the one-day fees 34 and 66 instead of the three-day totals (0.08m = 32). Choice B encodes adding the mileage rates instead of subtracting (0.32m = 96). Choice A encodes a decimal-place error, dividing 96 by 0.8 instead of 0.08.

Answer

A. 120 — Your setup 0.08m = 96 was right, but dividing by 0.8 instead of 0.08 shifted the decimal one place; 96/0.08 = 1,200.

Answer

B. 300 — You added the per-mile rates (0.20 + 0.12 = 0.32) instead of subtracting them; since the mileage terms are on opposite sides, you need 0.20m - 0.12m = 0.08m.

Answer

C. 400 — You used the one-day fees of $34 and $66, giving 0.08m = 32; the rental is 3 days, so the fixed costs are 3(34) = 102 and 3(66) = 198, making 0.08m = 96.

Algebra practice question

Answer: D. 1,200

Why the other answers are wrong

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