Reverse Percentage Problems

Students with poor understanding of the meaning of percentages find inverse percentage problems impossible. For example, finding the pre-discount price when, after a 15% discount, a  TV costs $350 is a challenging problem. Problems like this are easier to solve when percentages are converted to decimals before calculation.

Using Materials

Problem: “Pare receives a 15% discount on a TV, and he pays $510. What was the price  before the discount?”

Draw an empty flow chart on the board. Discuss  why the unknown full price is multiplied by  0.85.

Discuss why the full price is found by division,  and have the students calculate this price. (Answer: 510 ÷ 0.85 = $600.)

Problem: “Melissa buys blouses for her clothes  store. She marks the price up by 60%. If she sells a blouse for $74.25, how much did the blouse cost her?” Discuss why the flow chart shows that the cost price was 74.25 ÷ 1.60 = $46.41 (to the nearest  cent).

Using Imaging

Problem: “Janice adds GST of 12.5% to the price of a toaster. It now costs $31.50. What was the price of the toaster before GST was added?”
Imagine the flow chart and reverse it to find the answer.(Answer: $31.50 ÷ 1.125 = $28.00.)

Examples: Imagine flow charts. Fold back to drawing them if needed. Worksheet(Material Master 8–32).

Using Number Properties

Examples: Worksheet (Material Master 8–32).

Understanding Number Properties:

k% of the selling price $p is profit. What is the  cost price?
(Answer: $p(100-k) / 100 .)