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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

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