2008 AMC 12A Problem 3

Attempt Problem 3 of the 2008 AMC 12A 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 2008 AMC 12A solutions, or check the answer key.

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Suppose that

\tfrac{2}{3}

10

bananas are worth as much as

8

oranges. How many oranges are worth as much as

\tfrac{1}{2}

5

bananas?

2

\dfrac{5}{2}

3

\dfrac{7}{2}

4

First find how many oranges a single banana is worth

\tfrac{2}{3}

10

bananas is

\tfrac{20}{3}

bananas, and these equal

8

oranges

Since

\tfrac{2}{3}

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}

5

bananas is

\tfrac{5}{2}

bananas, worth

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

oranges.

Thus, C is the correct answer.

Problem 3 in other years