If a number(y) has 3% subtracted from it and you know the value of y, how can you find x

Question

I Get charged a 3% fee from my company from the entire fee collected (x) is not given without a lot of digging. I receive a Different amount each time which is y. For example I get paid 461.10 (y) one time and next time 577.50(y). What is the algebraic expression to figure out the original amount (x) before the 3% fee was removed? I can find out what x is on each transaction by digging. But...I have 75 transactions to dig through and algebra would help me find out quickly. In this case x is 480 and 600 respectively.

Answer 1

If you received $461.10 and your "x" was $480, then you're receiving 0.9606 of the 480 (461.10/480), which means a fee of 3.94%. (1 - 0.9606 = 0.394, or 3.94%)

If you received $577.50 from a base of $600, that's a fee of 3.75%. Don't know why they're different unless it's a rounding error.

Here's the algebra: Net Pay (y) = Base Pay (x) - (the fee at some percent (f)). The fee is f * x, or fx.

so y = x - fx. Factor out the x -> y = x(1-f), then x = y/(1-f). The fee (f) must be expressed as a decimal.

Example; 577.5/(1 - 0.0375) -> 577.5/0.9625 = 600 (base pay before the fee is taken out).

If the fee is really 3%, then use 0.97 as the factor.in the denominator.

Answer 2

You are receiving 97% of the fee each time. (The company gets the other 3%.)

Gross fee (what is paid by the customer) x 0.97 = Net fee (what you receive)

So Net fee = Gross fee/ 0.97

Simply divide whatever it is you receive each time by 0.97 to see what the original amount was.