2010 AMC 8 Problems/Problem 2

Problem

If $a @ b = \frac{a\times b}{a+b}$ for $a,b$ positive integers, then what is $5 @10$?

$\textbf{(A)}\ \frac{3}{10} \qquad\textbf{(B)}\ 1 \qquad\textbf{(C)}\ 2 \qquad\textbf{(D)}\ \frac{10}{3} \qquad\textbf{(E)}\ 50$

Solution

Substitute $a=5$ and $b=10$ into the expression for $a @ b$ to get:

$5 @ 10 = \frac{5\times 10}{5+10} = \frac{50}{15} = \frac{10}{3}$

Thus, answer choice $\boxed{\textbf{(D)}\ \frac{10}{3}}$ is correct.

See Also

2010 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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All AJHSME/AMC 8 Problems and Solutions

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