   SEARCH HOME Math Central Quandaries & Queries  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     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.