5. Discounts, Sale Prices, and Coupons

A discount lowers the original price. If an item is 25% off, the store removes 25% and you pay the remaining 75%.

Method 1 - subtract the discount:
\[ \text{discount}=0.25(80)=20,\qquad \text{sale price}=80-20=60. \]

Method 2 - pay the remaining percent:
\[ 75\%=0.75,\qquad 0.75(80)=60. \]

Both methods are correct. The second method is faster when you only need the final price.

Case study - stacked coupon warning: A store takes 20% off a 100 dollar item, then another 10% off the sale price. The price is not 70 dollars. First:
\[ 100(0.80)=80. \]
Then:
\[ 80(0.90)=72. \]
Sequential discounts apply to the new price each time.

Common mistake: adding discount percents without checking the base. 20% off then 10% off is not the same as 30% off when the second discount is applied after the first.