# 37.5 is 60% of what number?

Nov 16, 2016

37.5 is 60% of 62.5

#### Explanation:

First, let's call the number we are looking for $n$.

"Percent" or "%" means "out of 100" or "per 100", Therefore 60% can be written as $\frac{60}{100}$.

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

So, putting this all together allows us to write the following equation and solve for $n$ while keeping the equation balanced:

$\frac{60}{100} \times n = 37.5$

$\frac{100}{60} \times \frac{60}{100} \times n = \frac{100}{60} \times 37.5$

$1 \times n = \frac{3750}{60}$

$n = 62.5$

Nov 16, 2016

The number is 62.5

#### Explanation:

$\textcolor{b l u e}{\text{The general principle}}$

% is units of measurement and % is worth $\frac{1}{100}$

So 60% -> 60xx1/100 = 60/100

Using the principle of ratios, which really is the same thing as
smendyker used. It just looks different.

Consider $\frac{60}{100}$ as the reference ratio giving us:

$\frac{60}{100} \equiv \frac{37.5}{\text{some unknown value}}$

Let the unknown value be $x$ giving:

$\frac{60}{100} \equiv \frac{37.5}{x}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Building the conversion method}}$

These are ratios and equivalent to each other ( $\equiv$)

Then if I maintain the ratio but change the 60 into 37.5 I will find out what $x$ is worth.

Step 1: change 60 into 1$\to 60 \div 60 = 60 \times \frac{1}{60} = 1$

Step 2: multiply the 1 by 37.5$\to 60 \times \frac{1}{60} \times 37.5 = 60 \times \frac{37.5}{60}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Applying the conversion method}}$

Multiply by 1 but in the form of $1 = \frac{\textcolor{w h i t e}{.} \frac{37.5}{60} \textcolor{w h i t e}{.}}{\frac{37.5}{60}}$

color(green)([60/100color(magenta)(xx1)]->[60/100color(magenta)(xx(color(white)(.)37.5/60color(white)(.))/(37.5/60) ) ]#

$= \frac{37.5}{62.5}$

So the number is 62.5
...................................................................
That is: $\frac{60}{100} \times 62.5 = 37.5$