2008 AMC 12A Problems/Problem 3

Revision as of 15:03, 17 February 2008 by Xantos C. Guin (talk | contribs) (New page: ==Problem== Suppose that <math>\frac {2}{3}</math> of <math>10</math> bananas are worth as much as <math>8</math> oranges. How many oranges are worth as much is <math>\frac {1}{2}</math> ...)
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Problem

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

$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ \frac {5}{2} \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ \frac {7}{2} \qquad \textbf{(E)}\ 4$

Solution

If $\frac {2}{3} \cdot 10 \ \text{bananas} = 8 \ \text{oranges}$, then $\frac{1}{2} \cdot 5 \ \text{bananas} = \left(\frac{1}{2} \cdot 5 \ \text{bananas}\right) \cdot \left(\frac{8 \ \text{oranges}}{\frac {2}{3} \cdot 10 \ \text{bananas}}\right) = 3 \ \text{oranges} \Rightarrow C$.

See Also

2008 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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All AMC 12 Problems and Solutions