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Working from the selling price back to the original price

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

$S = $P(1 - 0.15)

$S = $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

$S ÷ 0.85 = $P × 0.85 ÷ 0.85

$S ÷ 0.85 = $P

$P = $S/0.85.

Thus if you divide the sale price by 0.85 (the % that you responsible for) you obtain the original price.

Find the original price for the following items.

1.) discounted price of a comic book: $3.95

12% discount was applied

2.) Price of a camera after tax is $554.65

8% tax was applied

3.) discounted price of a pair of shorts: $19.99

3/5 off as applied

4.) Price of a dinner after tax and tip is 156.45

30% tax and tip is applied

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