Reverse Percentages

Taylor receives 35% of a prize fund. If Taylor received $42, what was the total prize fund? How would we find 35% of something? We’d multiply by 0.35. Let’s guess. Maybe the answer is $110? 0.35 times 110 is $38.50. That’s not $42. But this shows us what we need: 0.35 times something equals 42. Let’s call the unknown x. In algebra we don’t write the times sign — we just put them next to each other. So we get: 0.35x equals 42. To solve, we do the opposite to both sides. Since it’s 0.35 times x, we divide both sides by 0.35. On the left, 0.35 divided by 0.35 cancels out, leaving just x. On the right, 42 divided by 0.35 is 120. x equals 120. The total prize fund was $120.

A café donates 15% of Saturday’s sales to charity. The donation was $27. What were the total sales? 15% as a decimal is 0.15. So our equation is 0.15x equals 27. Divide both sides by 0.15. The 0.15s cancel on the left, giving x. 27 divided by 0.15 is 180. Saturday’s total sales were $180.

12.5% of students at a school play rugby. 45 students play rugby. How many students attend the school? 12.5% as a decimal is 0.125. So: 0.125x equals 45. Divide both sides by 0.125. x equals 45 divided by 0.125, which is 360. There are 360 students at the school.