Subjects algebra

Coupon Comparison

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1. **Problem Statement:** We have four items with prices: Bike $140, Scarf $18, Winter Coat $75, and Book $12. There are two coupons: a 10% off coupon and a $10 off coupon. We want to find which coupon gives the lower price for each item. 2. **Formula for each coupon:** - Price after 10% off: $$\text{Price} - 0.10 \times \text{Price} = 0.90 \times \text{Price}$$ - Price after $10 off: $$\text{Price} - 10$$ 3. **Calculate prices for each item:** - Bike: 10% off = $0.90 \times 140 = 126$, $10 off = 140 - 10 = 130$ - Scarf: 10% off = $0.90 \times 18 = 16.20$, $10 off = 18 - 10 = 8$ - Winter Coat: 10% off = $0.90 \times 75 = 67.50$, $10 off = 75 - 10 = 65$ - Book: 10% off = $0.90 \times 12 = 10.80$, $10 off = 12 - 10 = 2$ 4. **Compare and mark better coupon:** - Bike: 10% off price $126$ is less than $130$, so 10% off is better. - Scarf: $10 off price $8$ is less than $16.20$, so $10 off is better. - Winter Coat: $10 off price $65$ is less than $67.50$, so $10 off is better. - Book: $10 off price $2$ is less than $10.80$, so $10 off is better. 5. **Final prices after better coupon:** - Bike: $126$ - Scarf: $8$ - Winter Coat: $65$ - Book: $2$ This shows that for expensive items like the bike, the percentage coupon saves more, but for cheaper items, the flat $10 off coupon is better.