How do i reverse this formula?

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Question from MK, a teacher:

Problem:
I have 22,000,000 worth of gold and wants to want to resell the gold back with a profit.
Each transaction of gold will have a transaction fee of 15%, so if i resell the gold back at 22,000,000, I will only get back 18,700,000 after 15% transaction cut.
The current formula is X-15%X = Y where X = 22,000,000 and Y = 18,700,000
Will u be able to come up with a new formula if we don't know the value of X but we know the value of Y
Something like this X-15%X = 22,000,000.
How do i reverse this formula to find the value of X?
Thanks

Hi,

A little bit of algebra gets you a long way in this problem. First of all $15\% = \frac{15}{100} = 0.15$ so you have

\[X - 0.15X = Y\]

On the left side $X$ is a common factor so the expression can be written

\[X(1 - 0.15) = Y.\]

But $1 - 0.15 = 0.85$ and hence

\[0.85 \times X = Y.\]

Filially divide both sides by $0.85$ to get

\[X = \frac{Y}{0.85}.\]

Thus for your example if $Y = 22,000,000$ then

\[X = \frac{22,000,000}{0.85} = 25,882,352.94\]

Penny

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