# 90 is 20% more than what?

Jan 7, 2017

See full explanation below:

#### Explanation:

We can write this as:

90 = x + (20% of x)

"Percent" or "%" means "out of 100" or "per 100", Therefore 20% can be written as $\frac{20}{100}$.

When dealing with percents the word "of" means "times" or "to multiply".

So we can rewrite the equation as and solve for $x$:

$90 = x + \left(\frac{20}{100} \times x\right)$

$90 = x + \frac{20}{100} x$

$90 = \frac{100}{100} x + \frac{20}{100} x$

$90 = \frac{120}{100} x$

$\frac{\textcolor{red}{100}}{\textcolor{b l u e}{120}} \times 90 = \frac{\textcolor{red}{100}}{\textcolor{b l u e}{120}} \times \frac{120}{100} x$

$\frac{9000}{\textcolor{b l u e}{120}} = \frac{\cancel{\textcolor{red}{100}}}{\cancel{\textcolor{b l u e}{120}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{120}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} x$

$75 = x$

$x = 75$

90 is 20% more than 75