Percentages

[LazyCarrot]

This is a 'real world' situation that I can never figure out mathematically
I always end up doing it by trial and error and its driving me nuts.
I just have a blind spot in figuring out the calculation.

I sell items on an online platform that takes a fixed percentage of the Sale Price for their fee.
If my Base Price is the amount I want to receive from the transaction,
and (x) is the percentage that the Platform wants to take from my Sale Price...
What is the percentage (y) that I need to increase my Base Price by
in order that I will receive the Base Price after the percentage (x) has been deducted from my Sale Price?

This is basically the same problem as calculating the amount of VAT to add to a Product Price in order that when the VAT is deducted from the Sale Price you receive the original Product Price.

 

[Prof]

To compute what you receive from the transaction, let S = the sale price. What would they do to the sale price to get your base pay B?
They take S and subtract x percent of S so S - xS = B. You can also solve this for S to get the sale price in relation to your base price.
S- xS = B so S(1 - x) = B and that makes S = B/(1 - x). For example if you want to receive a base price of 40 money units and they take out 20% or .20, then S = 40/(1 - .20) = 50. So if you tell them to charge 50 money units, then you will receive your 40 money units that you want. (I don't think you need the y that you mentioned.)

 

[LazyCarrot]

Thanks @Prof - that clears the fog! Much appreciated!