2008 AMC 12A Problem 3

Problem 3 of 25EasierArithmetic

Suppose that

\tfrac{2}{3}

of

10

bananas are worth as much as

8

oranges. How many oranges are worth as much as

\tfrac{1}{2}

of

5

bananas?

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Solution

Since

\tfrac{2}{3}

of

10

bananas is

\tfrac{20}{3}

bananas, worth

8

oranges, one banana is worth

8 \div \dfrac{20}{3} = \dfrac{24}{20} = \dfrac{6}{5}

oranges. Then

\tfrac{1}{2}

of

5

bananas is

\tfrac{5}{2}

bananas, worth

\dfrac{5}{2} \cdot \dfrac{6}{5} = 3

oranges. Thus, C is the correct answer.

Tagged: ratio and proportion

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