Discount and GST questions

A television has an original price of five hundred dollars. There's a 20 percent discount, and then 9 percent GST is added to the discounted price. How much does the customer pay? Let's draw the original price as one blue bar. This whole bar is the original price, five hundred dollars. The original price is the whole thing, so it's one hundred percent. We'll mark the line where one hundred percent ends. Now the discount. 20 percent off means 20 percent of the original price comes away. That's this part on the end, ringed in purple. So the customer doesn't pay one hundred percent. One hundred percent minus 20 percent leaves 80 percent, and 80 percent is what the customer pays. Let's work out 80 percent. One hundred percent is five hundred dollars, so 1 percent is five hundred dollars shared into one hundred. That's 5 dollars. 80 percent is 80 lots of that. Four hundred dollars. Or use the rule from before. 80 percent of five hundred dollars is 80 over one hundred, times five hundred. Cancel the one hundred into the five hundred, and that's 80 times 5. Four hundred dollars, the same answer. So the discounted price is four hundred dollars. Now the GST. Here's that same four hundred dollars again, on a new bar. GST is worked out on the price after the discount, so now four hundred dollars is the whole thing. It's the new one hundred percent. 9 percent GST is added on top, so the purple block goes past the one hundred percent line. One hundred percent and 9 percent more makes one hundred and nine percent. Let's work out one hundred and nine percent. One hundred percent is four hundred dollars, so 1 percent is 4 dollars. One hundred and nine percent is one hundred and nine times 4 dollars. That's four hundred and thirty-six dollars. By the rule, that is one hundred and nine over one hundred, times the discounted four hundred dollars. Not the five hundred. The four hundred is the whole thing now. The customer pays four hundred and thirty-six dollars.

Your turn. A fan is sold at 20 percent off. After the discount it costs two hundred and forty dollars. What was the original price? Remember, the two hundred and forty dollars is the 80 percent. Try it first. Pause if you like. Let's finish it. 80 percent is two hundred and forty dollars. So 1 percent is two hundred and forty dollars shared into 80. That's 3 dollars. The original price is the whole one hundred percent. One hundred times 3 dollars is three hundred dollars. So the fan was priced at three hundred dollars. So here's the rule. A discount means you pay less than one hundred percent. GST means you pay more than one hundred percent. Every time, ask which price the one hundred percent belongs to. That's the price the percentage is worked out on.