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

--------

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)

---------

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.

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.