At a sale, shirts were sold for $15 each. This price was 80% of their original price. What was the original price?

The #color(blue)"original price"# is 100%

and #80%=$15#

#rArr1%=($15)/80=$0.1875#

#rArr100%=$0.1875xx100=$18.75#

If you wish the above 2 operations may be combined into one.

original price #=($15)/80xx100=$18.75#

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.

#15/80 = x/100 " "rArr " " x = (15xx100)/80:" " x = $18.75#

Method 2: form an equation and solve it

Let the original amount be #x#

#80/100 xx x = 15" " rArr " "x = 15 xx 100/80 " "x = $18.75#

Method 3. Increase 15 in the ratio 100 : 80

#15 xx100/80 " " x = $18.75#

Method 4: unitary method

$15 represents 80%

#15/80 " represents " 1%#

#15/80 xx 100 " represents" 100%" " $18.75#

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.