# If a is 50% larger than c and b is 25% larger than c, then a is what percent larger than b?

Jun 22, 2016

$a$ is 20% larger than $b$

#### Explanation:

If $a$ is 50% larger than $c$
color(white)("XXX")a=150%xxc=3/2c
$\textcolor{w h i t e}{\text{XXX}} \rightarrow \textcolor{red}{c = \frac{2}{3} a}$

If $b$ is 25% bigger than $c$
color(white)("XXX")b=120%xxc= 5/4c
$\textcolor{w h i t e}{\text{XXX}} \rightarrow \textcolor{b l u e}{c = \frac{4}{5} b}$

Therefore
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{\frac{2}{3} a} = \textcolor{b l u e}{\frac{4}{5} b}$

$\textcolor{w h i t e}{\text{XXXX}} a = \frac{12}{10} b$
$\textcolor{w h i t e}{\text{XXXX}} = b + \frac{2}{10} b$
color(white)("XXXX") = b + (20%xxb)