a store adds 40% to a sale item. How can you find the origi
nal price (minus the 40 %) from the total sale price.

example: 10 + 40% = 14, but 14 - 40% does not equal 10?

Here's how to derive the equation to use: Given initial price P, price increase of i and a final price of F, you have

F = P(1+i)

using your example: P = $10, i = 40%, and F = $10(1+0.4) = $140.

Now let's take that equation and make P the subject by dividing both sides by (1+i):

\frac F {(1+i)} = P

This is the equation to use. So again, using your example: $140/(1+0.4) = $10.