Expert: Lynn Houston - 1/12/2010

Question
I had posed this question and didn't get a response.  "Our store has a sale on gift certificates of 15%.  Sometimes people want to spend a certain amount i.e. Mary wants to spend every penny of her $300.05 to get a certificate for $353.00.  ( Had this figured out by calculating backwards but need an actual formula) What formula do I use to figure out that $a-15%=$85 (solving for a)?"

and was asked on 01/04/2010
Let me rephrase.  We have 15% off gift certificate purchases.  Mary would like her final cost after discount to be $300.  Is the formula to figure her gift certificate value ( 300 divided by 85%= gift certificate value)?

Answer
Since you're using 2 sets of numbers, I'll just give you the formula and you can fill in any numbers you want.

Your first equation is correct.  you want to know what value of gift certificate - 15% if that value = a set amount.  Let's use $300 as the set amount.  So the eq would be

x - .15x = 300
.85x = 300 so
x = 300/.85 or 352.94