Problem 15 · 2010 AMC 8
Medium
Fractions, Decimals & Percents
find-total-from-percent
A jar contains five different colors of gumdrops: 30% are blue, 20% are brown, 15% red, 10% yellow, and the other 30 gumdrops are green. If half of the blue gumdrops are replaced with brown gumdrops, how many gumdrops will be brown?
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Answer: C — 42.
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Hint 1 of 2
The 30 green gumdrops are your only real count — everything else is a percent. So first turn green into a percent (whatever's left after the others), and it unlocks the total.
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Hint 2 of 2
‘A known count equals a known percent’ lets you find the whole: total = count ÷ (its percent). Once you have the total, every color becomes a real number.
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Approach: convert the one known count into the total
- The listed colors use 30+20+15+10 = 75%, so green is the remaining 25%. That 25% is the 30 green gumdrops, so the total = 30 / 0.25 = 120.
- Now percents become counts: blue = 30% · 120 = 36, brown = 20% · 120 = 24.
- Half the blue (18) turn brown: 24 + 18 = 42.
- Why this transfers: whenever a problem gives mostly percents and a single raw count, that count is your bridge — divide it by its percent to get the total, then read off the rest.
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