Question

50 is 125% of what number?

Answer 1

40

Explanation:

I like to solve these problems by translating it into math. The key words in this question are is and of. Is can be translated to `=` and of can be translated into multiplication. With these kinds of problems it's good to say "of means multiply". Now what number can be translated into a variable, I'll just use `x`.

Now we'll need to turn `125%` into a number we can work with. We can use `1.25` (divide the percentage by `100`) then turn `1.25` into `5/4` which will work nicely with the arithmetic for this problem.

So using that let's try to turn this into a problem we can solve for.

`50 = 5/4 * x`
`10=1/4 * x` (divide both sides by 5)
`40 = x` (multiply both sides by 4)

Answer 2

`x=40`

Explanation:

`color(blue)("The explanation bit about the method")`

Percentage can be presented in 2 ways.

Normally written in the form as `125%`

For mathematical purposes as `125/100`

Let the unknown value be `x`

The word in the question "of" really means multiply.
This is a bit like 2 of apples`->`2 apples`-> 2xx`apples

So 125% of unknown value is:

`125/100xx x`

We are told that the answer to this is 50 so we have

`125/100xx x =50`

To get `x` on its own the trick is to turn `125/100` into 1

What you do to 1 side of an equation you do to the other side.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("The calculation bit")`

`color(green)(125/100xx x= 50)`
`color(white)(.)`

Multiply both side by `color(red)(100/125)`

`color(green)(125/100color(red)(xx100/125)xx x=50color(red)( xx 100/125))`

`color(white)(.)`

But `125/100xx100/125" " ->" " 125/125xx100/100" " =" " 1`
`color(white)(.)`

`x=50xx100/125`

`x= 50/125xx100`

`x=2/(cancel(5)^1)xxcancel(100)^(20)`

`x=40`