Question

Tickets to The Phantom of the Opera just lowered 15%. If the new price is $51.00, what was the original price?

Answer 1

Then `$51.00` is `100%-15%=85%` of the original price.

Explanation:

Or:
`51div85=Xdiv100%->`

`85*X=100*51->X=(100*51)/85=$60`

Answer 2

`$60`

Explanation:

Here we have an example of reverse percentage. You know the amount AFTER a change has happened, but we do not know the starting amount.

The starting amount represents `100%` and the changed amount of `$51` represents `85% " from " 100%-15%`

You can use direct proportion because we are comparing percents and amounts.

`x/100 = 51/85" "(larr"amount in dollars")/(larr"percent")`

`85x = 51 xx100" "` by cross-multiplying

`x = (51xx100)/85`

`x = $60`

You could also have written the proportion in this form to get the same result:

`51/x = 85/100`