Problem 10 · 1996 AJHSME
Medium
Fractions, Decimals & Percents
fraction-of
When Walter drove up to the gasoline pump, his tank was 1/8 full. He bought 7.5 gallons, after which the tank was 5/8 full. How many gallons does the tank hold when it is full?
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Answer: D — 15 gallons.
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Hint 1 of 2
The 7.5 gallons didn't fill the tank — they filled the CHANGE in level, from 1/8 to 5/8. Subtract to see what fraction of the tank those gallons actually were.
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Hint 2 of 2
5/8 − 1/8 = 4/8 = half the tank was filled by 7.5 gallons. Once you know what fraction a known amount represents, scale up to the whole.
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Approach: the gallons fill the change in fraction
- The needle moved from 1/8 to 5/8, a change of 5/8 − 1/8 = 4/8 = half the tank. So 7.5 gallons is exactly half a tank.
- Double it: a full tank holds 2 × 7.5 = 15 gallons.
- Why this transfers: when an amount fills part of something, match it to the FRACTION that changed (not the start or end level), then scale: whole = amount ÷ fraction. Same move for 'tank,' 'recipe,' or 'discount left over.'
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