2014 AMC 10B Problem 7

Attempt Problem 7 of the 2014 AMC 10B 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 2014 AMC 10B solutions, or check the answer key.

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Suppose $A > B > 0$ and $A$ is $x\%$ greater than $B.$ What is $x?$

$100\left(\frac{A-B}{B}\right)$

$100\left(\frac{A+B}{B}\right)$

$100\left(\frac{A+B}{A}\right)$

$100\left(\frac{A-B}{A}\right)$

$100\left(\frac{A}{B}\right)$

Percent greater is measured relative to the smaller value $B$

First find the fraction $\frac{A-B}{B}$

By definition, we know $A = \dfrac {x+ 100}{100}B$ $= B + \dfrac x{100}B.$

This implies, $\begin{aligned} (A-B) &= \dfrac x{100}B\\ 100\left(\dfrac{A-B} B\right) &=x.\end{aligned}$

Thus, the correct answer is A .