If a @ b = (a× b/a+b) for a,b positive integers, then what is 5 @ 10 ?

AMC 8 2010 Problem 2

AMC8 2010 年第 2 题

表达式与运算★☆☆☆☆

If a @ b =

\displaystyle \frac{a\times b}{a+b}

for a,b positive integers, then what is 5 @ 10 ?

对于正整数

a

、

b

，定义

\displaystyle a @ b = \frac{a\times b}{a+b}

。那么 $5 @ 10$ 等于多少？

正确答案 · Correct Answer

Solution 1

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

\displaystyle 5 @ 10 = \frac{5×10}{5+10} = \frac{50}{15} = \frac{10}{3}

Thus, answer choice

\displaystyle \frac{10}{3}

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