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I want to sell something on eBay, but as you know they also take fees.

  • eBay Fees: 10%
  • PayPal 0,19%
  • PayPal 0,35€

Example: I want to make a profit (end price) of 16,18€ without fees.

I mean when you take the fees from that price ($x$) it should be 16,18€.

I tried the following formula, but it doesn't work.

$$x - 0{,}019x - 0{,}35 - 0{,}1x = 16{,}18$$

Please help me.

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    Does PayPal take its cut at the same time Ebay does or is one applied after the other one has already reduced your profit? – 2017-02-28

1 Answers 1

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You are almost there, up to a re-arrangement $$ x - 0.019x - 0.35 -0.1x = 16.18 $$ lets collect terms $$ x(1-0.019-0.1) -0.35 = 0.881x -0.35 = 16.18 $$ lets put similar terms together $$ 0.881x = 16.18 + 0.35 = 16.53 $$ now we need to get $x$ the price by itself so we need to do the opposite operation to multiplication, and this is division. $$ x = \dfrac{16.53}{0.881} = 18.762 $$ so the price you need to set is $18,77$ euros. (just to make sure you clear the rounding error to ensure the price you want)

This is assuming that we have linear deductions i.e. subtract $10$% for eBay, $0.19$% for PayPal and then the flat rate of $0.35$ all based on the original price, $x$.

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    Finally, thanks. – 2017-02-28
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    No problems! You did the hard part to be honest - modelling the problem in mathematics is normally the challenge. – 2017-02-28