2014 AMC 10B Problems/Problem 7: Difference between revisions

Revision as of 22:18, 24 October 2020

Problem

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

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

Solution

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

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

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

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

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

Solution 2

The question is basically asking the percentage increase from $B$ to $A$ . We know the formula for percentage increase is $\frac{\text{New-Original}}{\text{Original}}$ . We know the new is $A$ and the original is $B$ . We also must multiple by $100$ to get $x$ out of it's fractional/percentage form. Therefore, the answer is $100\left(\frac{A-B}{B}\right)$ or $\boxed{\text{A}}$ .

Video Solution

https://youtu.be/jj_rRTuWL14

~savannahsolver

2014 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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All AMC 10 Problems and Solutions

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 == Solution 2==
-The question is basically asking the percentage increase from <math>B</math> to <math>A</math>. We know the formula for percentage increase is <math>\frac{\text{New-Original}}{\text{Original}}</math>. We know the new is <math>A</math> and the original is <math>B</math>. We also must multiple by <math>100</math> to get <math>x</math> out of it's fractional/percentage form. Therefore, the answer is <math>100(\frac{A-B}{B})</math> or <math>\boxed{\text{A}}</math>.
+The question is basically asking the percentage increase from <math>B</math> to <math>A</math>. We know the formula for percentage increase is <math>\frac{\text{New-Original}}{\text{Original}}</math>. We know the new is <math>A</math> and the original is <math>B</math>. We also must multiple by <math>100</math> to get <math>x</math> out of it's fractional/percentage form. Therefore, the answer is <math>100\left(\frac{A-B}{B}\right)</math> or <math>\boxed{\text{A}}</math>.
 ==Video Solution==

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