2008 AMC 12A Problem 3

Below is the professionally curated solution for Problem 3 of the 2008 AMC 12A, 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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Concepts:ratio and proportion

Difficulty rating: 1100

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?

$2$

$\dfrac{5}{2}$

$3$

$\dfrac{7}{2}$

$4$

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.

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