2014 AMC 10B Problems/Problem 7

Problem

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

$\textbf {(A) } 100(\frac{A-B}{B}) \qquad \textbf {(B) } 100(\frac{A+B}{B}) \qquad \textbf {(C) } 100(\frac{A+B}{A})\qquad \textbf {(D) } 100(\frac{A-B}{A}) \qquad \textbf {(E) } 100(\frac{A}{B})$

Solution

We have that A is $x\%$ greater than B, so $A=\frac{100+x}{100}(B)$ . We solve for $x$ . We get

$\frac{A}{B}=\frac{100+x}{100}$

$100\frac{A}{B}=100+x$

$100(\frac{A}{B}-1)=x$

$(\textbf{A}) \boxed{100(\frac{A-B}{B}) }=x$ .

2014 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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2014 AMC 10B Problems/Problem 7

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