Problem 7 · 2026 AMC 8
Medium
Fractions, Decimals & Percents
fraction-of
Mika wants to estimate how far a new electric bike goes on a full charge. She made two trips totaling 40 miles: the first used 12 of the battery and the second used 310 of the battery. How many miles can the bike go on a fully charged battery?
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Answer: C — 50 miles.
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Hint 1 of 2
The 40 miles didn't drain a full battery. First combine the two trips: what single fraction of the battery did the 40 miles actually use?
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Hint 2 of 2
Once you know 40 miles used some fraction of the charge, the rest is one proportion: scale that fraction up to a whole battery (the full charge is 5/5).
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Approach: find the fraction the 40 miles used, then scale to a whole battery
- Combine the two trips: ½ + 3/10. With a common denominator, 5/10 + 3/10 = 8/10 = 4/5 of the battery powered the 40 miles.
- If 4/5 of a charge gives 40 miles, each fifth gives 40 ÷ 4 = 10 miles, so a full 5/5 gives 5 × 10 = 50 miles.
- Why this works: ‘a fraction of the whole equals a known amount’ is a proportion — find the value of one unit piece (here, one-fifth = 10 mi), then multiply up to the whole.
Another way — divide by the fraction:
- 4/5 of the battery = 40 miles, so the full battery is 40 ÷ 45 = 40 × 54 = 50 miles.
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