Question

Question #2517c

Answer 1

This is a 25% discount.

Explanation:

We can restate this problem as:

$13 is what percent of $52?

First, lets call the percent we are looking for "p" or `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:

`$13 = p/100 xx $52`

`$13 = ($52p)/100`

`$13 xx color(red)(100/($52)) = ($52p)/100 xx color(red)(100/($52))`

`($1300)/($52) = ($52p)/100 xx 100/($52)`

`(color(green)(cancel(color(black)($)))1300)/(color(green)(cancel(color(black)($)))52) = (color(blue)(cancel(color(black)($52)))p)/color(red)(cancel(color(black)(100))) xx color(red)(cancel(color(black)(100)))/(color(blue)(cancel(color(black)($52))))`

`1300/52 = p`

`25 = p`