Question

40 is what percent of 32?

Answer 1

40 is `color(red)(125%)` of 32

Explanation:

First, lets call the percent we are looking for "p".

"Percent" or "%" means "out of 100" or "per 100", Therefore p% can be written as `p/100`.

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

Putting this altogether we can write this equation and solve for `p` while keeping the equation balanced:

`40 = p/100 xx 32`

`color(red)(100)/color(blue)(32) xx 40 = color(red)(100)/color(blue)(32) xx p/100 xx 32`

`4000/color(blue)(32) = cancel(color(red)(100))/cancel(color(blue)(32)) xx p/color(red)(cancel(color(black)(100))) xx color(blue)(cancel(color(black)(32)))`

`125 = p`

`p = 125`

Answer 2

125%.

Explanation:

Translate from words to math:

`"40 is what percent of 32"`

`40=x xx 1/100xx32`

`40=(32x)/100`

`(40xx100)/32=x`

`125=x`

You can also think of it as this:

32 is like our whole. It's like our 100%. So 32 is to 100% as 40 is to what percent?

`32/(100%)=40/x`

`32x=40(100%)`

`x=(40(100%))/32`

`x=125%`