Determining a discount dollar amount

• Aug 15th 2013, 08:23 AM
aasmith26
Determining a discount dollar amount
Hello, everyone! I bring a challenging question to you all. I am trying to come up with an equation to help me and one of my coworkers solve this problem.

Here are some numbers.

Original Retail Price: \$448.00
Tax: (6%) 26.88
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Total: 474.88

Now, the new order info is as follows. I need to find out how to calculate the difference I need to deduct after applying another 10% discount.

New Retail: \$549.00
Amount to Discount (?) -51.22 (we'll call this X)
New Total: 497.78
Additional 10% off of new total -49.78 (Y)
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Subtotal: 448.00 (essentially matching the above original retail before tax)
Tax: (6%) 26.88
Total Due: \$ 474.88 (must match same as previous total due)

My ultimate goal is to find out how I get X and/or Y. I am applying a 10% coupon afterwards, but need to enter the discount difference to come up with the same total due as the previous total due.

Is there a formula I could use?
Any help would be appreciated.
• Aug 15th 2013, 08:40 AM
HallsofIvy
Re: Determining a discount dollar amount
So you are saying that you want to start with 549, subtract some quantity "X" then take 10% of that (Y) to get 474.88 still?

Okay, taking X from 549 leaves 547- X and 10% of that is .10(547- X)= 54.7- X/10. So subtracting that from 547- X leaves 547- X- 54.7+ X/10= 492.3- (9/10)X= 474.88. To solve that subtract 474.88 and add (9/10)X from both sides to get (9/10)X= 492.3- 474.88= 17.42. Now multiply on both sides by 10/9: X= (17.42)(10/9)= 174.2/9= 19.35555... which you could round to X= \$19.36. Y= (.10)X= \$1.94.