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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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