Getting confused why i dont get expected amount?

Question

I have 1 result and which i will receive in Bank account, Based on that account i have to Put a balance to user account.

How can you find the Handling cost from total tried 491.50 / 0.95 = 517.36 which is wrong ? It should be 500.00 (to my expectation)

User balance requires 500.00 When 500.00 selected he gets 5% discount There is a handling cost for this

ex:
1) Discount: 500.00 - 5% = 475.00    
2) Handling cost: (475.00 x 0.034) + 0.35 = 16.50   
3) Total: 475.00 + 16.50 = 491.50

So problem is from 491.50, i have to find atleast handling cost to get promised Balance.

Any solution ? Cant figure it out myself...

In short cut: a) i put 491.50 -> b) my formula will suggest me apply balance 500.00 (which is the main goal)

Answer 1

(final_price - 0.35) / 1.034 / 0.95

For 491.50, this yields 500.

You might try to combine the last 2 divisions to be divide by 1.034 * 0.95 = 0.9823, but you will have to guard against rounding errors due to using floating point arithmetic.

Answer 2

So, your maths can be represented as:

((0.95 * initialCost * 0.034) + 0.35) + (0.95 * initialCost ) = finalCost

which reduces to

(0.9823 * initialCost) + 0.35 = finalCost

It follows that

initialCost = (finalCost - 0.35) / 0.9823