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Question 17 Chau has two coupons for shoes. Coupon A: \( \$ 15 \) rebate on \( \$ 75 \) shoes Coupon \( B: \quad 25 \% \) off of \( \$ 75 \) shoes Choose the coupon that gives the lower price. Then fill in the blank with the correct value. The price with coupon \( A \) is \( \$ \square \) less than the price with coupon \( B \). Coupon B gives the lower price. The price with coupon B is \( \$ \square \) less than the price with coupon \( A \).

Ask by Warner Weaver. in the United States
Jan 24,2025

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Coupon B gives the lower price. The price with coupon B is $3.75 less than the price with coupon A.

Solución

Let's evaluate both coupons to determine which one offers the better deal. **Coupon A: $15 Rebate on $75 Shoes** - **Discount:** \$15 - **Final Price:** \$75 - \$15 = **\$60** **Coupon B: 25% Off on $75 Shoes** - **Discount:** 25% of \$75 = 0.25 × \$75 = **\$18.75** - **Final Price:** \$75 - \$18.75 = **\$56.25** **Comparison:** - **Coupon B** offers a lower final price (\$56.25) compared to **Coupon A** (\$60). - The difference between the two coupons is \$60 - \$56.25 = **\$3.75**. **Filled-in Blanks:** - The price with coupon ***B*** is **\$3.75** less than the price with coupon ***A***. --- **Final Answer:** Coupon B gives the lower price. The price with coupon B is $ 3.75 less than the price with coupon A.

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The Deep Dive

To compare the two coupons, let’s calculate the final prices with each coupon on a pair of shoes that costs $75. For Coupon A: - Price with Coupon A = Original Price - Rebate = \( 75 - 15 = \$ 60 \). For Coupon B: - Discount = 25% of $75 = \( 0.25 \times 75 = 18.75 \). - Price with Coupon B = Original Price - Discount = \( 75 - 18.75 = \$ 56.25 \). Now, comparing the two prices: - The price with Coupon A is \( \$ 60 - \$ 56.25 = \$ 3.75 \) more than the price with Coupon B. - Therefore, Coupon B gives the lower price. The final answers are: The price with coupon \( A \) is \( \$ 3.75 \) less than the price with coupon \( B \). Coupon B gives the lower price. The price with coupon B is \( \$ 3.75 \) less than the price with coupon \( A \).

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