   SEARCH HOME Math Central Quandaries & Queries  Question from Debra, a student: Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him? Hi Debra, How does Jim calculate the selling price? Suppose the statue originally cost him$500. He adds 35% of is cost to arrive at the selling price, that is

his cost + 35% of his cost = selling price                 (1)

which is

$500 + 0.35 ×$500 = selling price
$500 +$175 = selling price
$675 = selling price. This is not your question however. What you have is the percentage profit (35%) and the selling price (in my case$675) and you want to know his cost. Look at equation (1) again. With my numbers it becomes

his cost + 35% of his cost = $675. Let his cost be$C then this is

$C + 0.35 ×$C = $675 (1 + 0.35) ×$C = $675 (1.35) ×$C = $675 so$C = $675/1.35 =$500.

Now try it with your numbers,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.