Math CentralQuandaries & Queries


Question from Cyndy, a parent:

Find the original price of a pair of shoes if the sale price is $98.00 after a 30% discount.


If you know the original price and the discount percent you can calculate the sale price. A little algebra then lets you turn this around and calculate the original price if you know the discount percent and the sale price. Here is an example.

Suppose the original price of a pair of shoes is $80.00 and it is on sale for 15% off. The discount is then 15% of $80.00 or $80.00 × 0.15 and the sale price is

sale price = $80.00 - $80.00 × 0.15.

You can now do the arithmetic to find the sale price.

Let's now introduce some algebra. If the original price is $P and the sale price is $S and the discount rate is still 15%. The discount is $P × 0.15 and hence the sale price is given by

$S = $P - $P × 0.15 = $P(1 - 0.15) = $P × 0.85.

Now I hope you can see what to do. If

$S = $P × 0.85

and you divide both sides by 0.85 you get

$P = $S/0.85.

Thus if you divide the sale price by 0.85 you obtain the original price.

Now try this technique with your problem and write back if you need further help.


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