The Discount Stack
A jacket has a list price of $80. A store offers a 25 percent discount on the jacket. Separately, a coupon gives $10 off any purchase over $50, applied after the percentage discount. A customer also has a store loyalty card that gives 5 percent off the final price after all other discounts. The customer wants to know the final price and whether it is cheaper to apply the coupon before or after the 25 percent discount. Sales tax of 8 percent is added to the final discounted price.
1. Compute the final price with tax, applying discounts in the stated order.
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Start: $80. 25 percent off: 80 × 0.75 = $60. Coupon $10 off: 60 − 10 = $50. Loyalty 5 percent: 50 × 0.95 = $47.50. Tax 8 percent: 47.50 × 1.08 = $51.30. Final price: $51.30.
2. Is the coupon cheaper before or after the 25 percent discount? Show the comparison.
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Coupon after discount (stated order): 80 → 60 → 50 → 47.50 → with tax $51.30. Coupon before discount: 80 − 10 = 70; 25 percent off: 70 × 0.75 = 52.50; loyalty 5 percent: 52.50 × 0.95 = 49.875; tax: 49.875 × 1.08 = 53.865, about $53.87. So applying the coupon after the percentage discount is cheaper ($51.30 vs about $53.87). Reason: a fixed $10 taken off a smaller base removes a larger share, and the later percentage discounts then compound on a smaller number.