2007 AMC 8 Problem 17

Attempt Problem 17 of the 2007 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

17.

A mixture of 3030 liters of paint is 25%25\% red tint, 30%30\% yellow tint and 45%45\% water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture?
2525
3535
4040
4545
5050
Answer: C
Concepts:mixturepercentage
Small hint:
Find the original number of liters of yellow tint.
Big hint:
After adding yellow tint, both the yellow amount and the total mixture amount change.
Solution:
The amount of yellow tint in the original mixture is 0.3×30=90.3 \times 30 = 9 liters. Adding 55 liters results in a total of 1414 liters of yellow tint.
The new mixture has a total of 3535 liters, so the percent of yellow tint is 100⋅1435=100⋅25=40%. 100 \cdot \dfrac{14}{35} = 100 \cdot \dfrac{2}{5} = 40 \%.
Thus, C is the correct answer.
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