Problem 17 · 2007 AMC 8
Easy
Fractions, Decimals & Percents
mixture-update
A mixture of 30 liters of paint is 25% red tint, 30% yellow tint and 45% water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture?
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Answer: C — 40%.
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Hint 1 of 2
Percentages of a changing total are slippery — switch to actual liters. Pouring in yellow grows the yellow and the whole batch, so both the top and bottom of the fraction move.
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Hint 2 of 2
Convert percents to amounts before mixing: track the quantity you care about and the total separately, then re-form the percent at the end.
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Approach: switch to liters, update both parts
- Yellow at the start: 30% of 30 = 9 L. (The red and water percents are scenery — ignore them.)
- Add 5 L of yellow: yellow becomes 9 + 5 = 14 L, and the whole batch grows to 30 + 5 = 35 L.
- New yellow percent = 14/35 = 2/5 = 40%.
- Common trap: the answer isn't 30% + something simple — you must enlarge the denominator too. Yellow jumped from 9/30 to 14/35 because both numbers changed.
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