Problem 12 · 1999 AMC 8
Medium
Fractions, Decimals & Percents
ratio-to-percent
The ratio of the number of games won to the number of games lost (no ties) by the Middle School Middies is 114. To the nearest whole percent, what percent of its games did the team lose?
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Answer: B — 27%.
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Hint 1 of 2
A ratio of 11 to 4 isn't 11 games and 4 games — it's 11 parts to 4 parts. The whole is the parts added: 11 + 4 = 15. Percent-lost is the lost parts over the whole.
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Hint 2 of 2
Percent-of-the-whole always needs the WHOLE in the denominator. The ratio's denominator (4 lost) is not the total — add the parts to get it.
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Approach: ratio → parts → fraction of the whole → percent
- Read the ratio as parts: 11 won-parts and 4 lost-parts, so the whole is 11 + 4 = 15 parts. Losses are 4 of those 15.
- 4/15 = 0.2666… ≈ 26.7%, which rounds to 27%.
- The classic trap this dodges: the answer is NOT 4/11 (lost vs won) — percent of games requires lost over total games, so you must sum the parts first. Choice A (24% ≈ 4/16.7) and E (73%, the win rate) are there to catch that slip.
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