1996 AMC 8 Problem 10

Attempt Problem 10 of the 1996 AMC 8 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 1996 AMC 8 solutions, or check the answer key.

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

10.

When Walter drove up to the gasoline pump, he noticed that his gasoline tank was 18\dfrac18 full. He purchased 7.57.5 gallons of gasoline for $10.\$10. With this additional gasoline, his gasoline tank was then 58\dfrac58 full. The number of gallons of gasoline his tank holds when it is full is
8.758.75
1010
11.511.5
1515
22.522.5
Answer: D
Concepts:fractionratio and proportion
Small hint:
Going from 18\dfrac18 to 58\dfrac58 full is an increase of 12\dfrac12 of a tank
Big hint:
If half a tank is 7.57.5 gallons, double it for a full tank
Solution:
The increase is 58−18=12\dfrac58 - \dfrac18 = \dfrac12 of a tank, which equals 7.57.5 gallons.
So a full tank holds 2⋅7.5=152 \cdot 7.5 = 15 gallons.
Thus, the correct answer is D .
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