Each price has its own 100 percent

A television has an original price of five hundred dollars. The shop gives a twenty percent discount, and then nine percent GST is added to the discounted price. How much does the customer pay? We start with the television’s original price. The whole five hundred dollars is one hundred percent. Twenty percent off is this part at the end. One hundred percent minus twenty percent leaves eighty percent to pay. One percent is five hundred dollars divided by one hundred, which is five dollars. Eighty percent is eighty times five dollars, which is four hundred dollars. The percentage rule gives the same answer: eighty percent of five hundred dollars is eighty over one hundred times five hundred dollars. Divide the denominator one hundred and the factor five hundred by one hundred. They become one and five. Eighty times five dollars is four hundred dollars. For GST, copy that same four hundred dollars to a new row. GST is charged on the discounted price. Four hundred dollars is the new one hundred percent. Add nine percent GST to this new whole. One hundred percent plus nine percent is one hundred and nine percent. One percent is four hundred dollars divided by one hundred, which is four dollars. One hundred and nine percent is one hundred and nine times four dollars, which is four hundred and thirty six dollars. By the percentage rule, one hundred and nine over one hundred times the discounted four hundred dollars also gives four hundred and thirty six dollars. The customer pays four hundred and thirty six dollars. The discounted bar stops short of its original one hundred percent. The GST bar extends beyond its new one hundred percent.

Now try the reverse. A ceiling fan is sold at a twenty percent discount. After the discount it costs two hundred and forty dollars. What was the original price of the fan? One hundred percent minus twenty percent leaves eighty percent. The two hundred and forty dollars is eighty percent of the original price. Try it first. Pause if you like. One percent is two hundred and forty dollars divided by eighty, which is three dollars. The original price is one hundred times three dollars, which is three hundred dollars. The fan’s original price was three hundred dollars. Always identify the price that represents one hundred percent before calculating.