2. Markup, Discounts, and Sale Prices

Stores change prices by a percent. To increase a price by \(p\%\), multiply by \(\left(1 + \dfrac{p}{100}\right)\); to discount it, multiply by \(\left(1 - \dfrac{p}{100}\right)\).

Worked example (markup): A store buys a jacket for $40 and marks it up 60%. The selling price is
\[ 40 \times (1 + 0.60) = 40 \times 1.60 = 64 \text{ dollars.} \]

Worked example (discount): A $90 pair of shoes is 25% off. The sale price is
\[ 90 \times (1 - 0.25) = 90 \times 0.75 = 67.50 \text{ dollars.} \]

Working backward: a shirt is on sale for $48 after a 20% discount. If \(x\) is the original price, then \(0.80x = 48\), so \(x = \dfrac{48}{0.80} = 60\) dollars.

The multiplier trick is faster than finding the dollar change and then adding or subtracting — one multiplication gives the final price.