2014 AMC 10B Problem 7

Problem 7 of 25EasierAlgebra

Suppose

A > B > 0

and

A

x\%

greater than

B.

What is

x?

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Solution

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 .

Concepts: percentage · algebraic manipulation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.