Question

Work with a partner. You buy a shirt that is on sale for 30% off. You pay $22.40. Your friend wants to know the original price of the shirt. How can your friend find the original price?

Answer 1

`$32.00`

Explanation:

Let's turn that percentage into a decimal so it is easier to work with.

`30-:100= 0.3`

So... we know that `$22.40` is `70%` of our original price since we took away `30%` from the original to get to `$22.40`

That means that `70%` of `x` price that we don't know should equal `22.40` or...

`0.7x=22.40`

[Don't forget you can divide any percentage by 100 to turn it into a decimal]

Now we just solve our equation to find `x` which is our original price

`0.7x=22.40`

Divide both sides by `0.7`

`(0.7x)/0.7=22.40/0.7`

`(cancel0.7x)/cancel0.7=22.40/0.7`

`x=22.40/0.7`

`x=32`

We can even check our answer.

Take our total price `32` and take away `30%` from it to see if we get back to `22.40`

[`30%=0.3`]

`$32*0.3=$9.6`

So `30%` of `$32` is `$9.6`. Take those `$9.6` dollars away from our `$32` to see if we are back where we started.

`$32-$9.6=$22.40`

`$22.40`