At a sale, shirts were sold for $15 each. This price was 80% of their original price. What was the original price?
#color(blue)"original price"#is 100%
If you wish the above 2 operations may be combined into one.
Do not be tempted to increase $15 by 20% thinking that will make the original 100%. 20% of the original amount and 20% of the reduced amount are different quantities.
There are several different approaches:
Method 1: direct proportion
Compare the values with their corresponding percentages.
Method 2: form an equation and solve it
Let the original amount be
Method 3. Increase 15 in the ratio 100 : 80
Method 4: unitary method
$15 represents 80%
Notice that in each case, although the approach and reasoning were different, the calculations and the answer were the same.
The important thing is to recognise that this is a reverse percentage calculation, because the original amount is not known.