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

##### 2 Answers

$ 18.75

#### Explanation:

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#

#### Explanation:

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.