2014 AMC 10A Problem 1

Problem 1 of 25EasierAlgebra

What is the value of the following expression?

10\cdot\left(\dfrac{1}{2}+\dfrac{1}{5}+\dfrac{1}{10}\right)^{-1}

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Solution

We get that

\begin{aligned} &\dfrac{1}{2} + \dfrac{1}{5} + \dfrac{1}{10} \\ &= \dfrac{5}{10} + \dfrac{2}{10} + \dfrac{1}{10} \\&= \dfrac{4}{5}. \end{aligned}

Then

\left(\dfrac{4}{5}\right)^{-1} = \dfrac{5}{4}

and then finally,

10 \cdot \dfrac{5}{4} = \dfrac{25}{2}.

Thus, C is the correct answer.