Question

37.5 is 60% of what number?

Answer 1

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 `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:

`60/100 xx n = 37.5`

`100/60 xx 60/100 xx n = 100/60 xx 37.5`

`1 xx n = 3750/60`

`n = 62.5`

Answer 2

The number is 62.5

Explanation:

`color(blue)("The general principle")`

% is units of measurement and % is worth `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 `60/100` as the reference ratio giving us:

`60/100-=37.5/("some unknown value")`

Let the unknown value be `x` giving:

`60/100-=37.5/x`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Building the conversion method")`

These are ratios and equivalent to each other ( `-=`)

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`->60 -:60 = 60xx1/60 = 1`

Step 2: multiply the 1 by 37.5`-> 60xx1/60xx37.5 = 60xx37.5/60`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Applying the conversion method")`

Multiply by 1 but in the form of `1=(color(white)(.)37.5/60color(white)(.))/(37.5/60)`

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

`=37.5/62.5`

So the number is 62.5
...................................................................
That is: `60/100xx62.5 = 37.5`