Percentages

Concept

Three ideas you'll use over and over:

• p% of N — (p/100) · N.
• Percent change — (new − old) / old × 100%.
• Increase / decrease — multiply by (1 + p/100) for an increase, (1 − p/100) for a decrease.

Successive percent changes don't add. A 10% increase followed by a 10% decrease gives 1.10 × 0.90 = 0.99 — a net 1% decrease. This is a classic SAT trap.

To recover the original after a percent change: divide by the multiplier. e.g. after a 25% discount, the sale price is 0.75 × original, so original = sale / 0.75.

Worked example 1

After a 30% discount, a jacket costs $42. What was the original price?

Worked example 2

A product's price went from $50 to $65. Find the percent change.