2008 AMC 10A Problem 4 — Solution | LIVE by Po-Shen Loh

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2008 AMC 10A Problem 4

Attempt Problem 4 of the 2008 AMC 10A 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 10A solutions, or check the answer key.

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

4.

Suppose that $\dfrac{2}{3}$ of $10$ bananas are worth as much as $8$ oranges. How many oranges are worth as much as $\dfrac{1}{2}$ of $5$ bananas?

$2$

$\dfrac{5}{2}$

$3$

$\dfrac{7}{2}$

$4$

Answer: C

Concepts:ratio and proportion rate

Difficulty rating: 1040

Solution:

Since $\dfrac{2}{3}$ of $10$ bananas is $\dfrac{20}{3}$ bananas worth $8$ oranges, one banana is worth $8 \div \dfrac{20}{3} = \dfrac{6}{5}$ oranges.

Now $\dfrac{1}{2}$ of $5$ bananas is $\dfrac{5}{2}$ bananas, worth $\dfrac{5}{2} \cdot \dfrac{6}{5} = 3$ oranges.

Thus, the correct answer is C.

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Problem 4 in Other Years

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