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2005 AMC 10B Problem 3

Problem 3 of 25EasierAlgebra

A gallon of paint is used to paint a room. One third of the paint is used on the first day. On the second day, one third of the remaining paint is used. What fraction of the original amount of paint is available to use on the third day?

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Solution

After the first day, 113=231 - \dfrac13 = \dfrac23 of the paint remains. On the second day, 1323=29\dfrac13 \cdot \dfrac23 = \dfrac29 of the original amount is used. The fraction available on the third day is 2329=49. \dfrac23 - \dfrac29 = \dfrac49. Thus, D is the correct answer.

More practice

Concepts: fraction · ratio and proportion

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