2470.21 – The Barbell Exchange

My uncle sold a set of barbells for 99 dollars and made a 10 percent profit. He sold a second set for 99 dollars but this time took a 10 percent loss. Putting the two sales together, did he gain, lose, or come out even?

Solution

Let $x$ be the cost of the first set of weights. Now, selling price = cost + profit, so

$99 = x + 0.10 x = 1.1 x$

From this we deduce that $x = 90$ so my uncle made 9 dollars on this sale. Let $y$ be the cost of the second set of weights. Arguing similarly,

$99 = y - .1 y = .9 y$

so $y$ is 110 dollars. On this sale my uncle had an 11 dollar loss. All-in-all, he had a 2 dollar loss. :(