# 8.1.21 Working Backwards

In some situations, you may be given the total after the discount or tax has been applied and asked to find the original amount. For example, suppose an online store charges an extra 5% of the cost of the purchases for postage and packing. You have a gift voucher for $30. What is the maximum you can spend at the store, so that the total including the postage is less than$30?

As you can see in the diagram above, 105% is equivalent to $30. Therefore, 1% is equivalent to , and multiplying this quotient by 100 creates 100%, which results in (rounded down to the nearest cent). The maximum amount that can be spent then is$28.57. You can check your answer by working out the 5% postage charge on $28.57 to see that the grand total will be$30.

## Activity: Working Backwards

The price of a tennis racquet, including a 4% sales tax, is $45.24. What was the price before sales tax? ### Comment The$45.24 includes sales tax. What percentage does this total represent? Find the dollar amount that represents 1%, and use that figure to arrive at 100%.

104% of the cost is $45.24. 1% is and 100% is . Thus, the price of the tennis racquet before sales tax was applied was$43.50.