Figure out an exact amount to charge before service fee to get specific amount after

[TK12]

Hi Everyone,
My question is a real life problem I have but it seems like it would fit in this section.. I need to collect money using a square card reader. The problem is square takes 2.75% of the charged amount and I need to collect exact amounts after that service charge. So I need a formula to figure out how much to charge BEFORE the fee in order to get exact amounts AFTER the fee.

My problem is I don't know a better way to go about it, and I can't solve my formula.

'w'= wanted amount of money after the service fee
'c'= amount I need to charge before the fee

w=c-(c*.0275)
If I set up this equation I need to solve for 'c' in terms of 'w'


However maybe there is a better way?
I have also thought about doing something with 102.75% or 97.25%, but I can't figure out how those numbers would help me. Is it possible to solve this formula? Or is there another way to set it up?

I also thought about using a ratio as a possibility, but I'm not sure how I could use one. I was thinking maybe something like the following would work, not sure:
c/97.25%=w/100 these are just some random thoughts I had in my head.

Please help me figure this problem out!
Thanks in advance!

 

[JeffM]

Hi Everyone,
My question is a real life problem I have but it seems like it would fit in this section.. I need to collect money using a square card reader. The problem is square takes 2.75% of the charged amount and I need to collect exact amounts after that service charge. So I need a formula to figure out how much to charge BEFORE the fee in order to get exact amounts AFTER the fee.

My problem is I don't know a better way to go about it, and I can't solve my formula.

'w'= wanted amount of money after the service fee
'c'= amount I need to charge before the fee

w=c-(c*.0275)
If I set up this equation I need to solve for 'c' in terms of 'w'


However maybe there is a better way?
I have also thought about doing something with 102.75% or 97.25%, but I can't figure out how those numbers would help me. Is it possible to solve this formula? Or is there another way to set it up?

I also thought about using a ratio as a possibility, but I'm not sure how I could use one. I was thinking maybe something like the following would work, not sure:
c/97.25%=w/100 these are just some random thoughts I had in my head.

Please help me figure this problem out!
Thanks in advance!

\(\displaystyle c - 0.0275c = w \implies 0.9725c = w \implies c = \dfrac{w}{0.9725}.\) Your math intuition is fine.

But this formula will not come out to an even number every time. I suggest you round everything up.

If you are using excel, the formula for rounding up is ceiling. Try using .01 for significance.

Let us know if you need more help.