Simple commission calculation, explanation

Hi all, I am having a bit of a hard time getting my head around this simple calculation:

The question expresses, if a individual withdrew $780 in cash from an ATM, how much has he spent in total, expressed in Pounds Sterling?

Cash withdrawal (ATM) Commision 2.50% with a fee of 9GBP. Exchange rate of 1.7USD=1GBP.

There are two ways I thought I could calculate the total charge, however they seem to come with different answers which I found very difficult to understand why they are different.

x=Total Pounds Sterling.

(x-9)*1.7*0.975=780
x=479.59

((780*1.025)/1.7)+9=x
x=479.29

These calculations are pretty much the same, at least in logic, the first being working out x (total spent), the second working backwards....

So why is there are ±0.3 difference?

Because 780*1.025 is not the same as 780/.975

I understood that, I am asking, why in pure logic thinking, does it not workout the other way around?

(x-9)*1.7*0.975=780
x=479.59

In the first case I deducted the fee for transaction, then exchange rate and commision was taken from total value. Though the answer is not the same as the one below

((780*1.025)/1.7)+9=x
x=479.29

First taken the total amount in GBP with commision and plus the fee for transaction.

Logic seems fine in both, but answer does not equate.

I understood that, I am asking, why in pure logic thinking, does it not workout the other way around?

(x-9)*1.7*0.975=780
x=479.59

In the first case I deducted the fee for transaction, then exchange rate and commision was taken from total value. Though the answer is not the same as the one below

((780*1.025)/1.7)+9=x
x=479.29

First taken the total amount in GBP with commision and plus the fee for transaction.

Logic seems fine in both, but answer does not equate.