14. Multistep A clothing store has the sign shown in the snop wind Pani sees the sign and wants to buy 3 shirts and 2 pairs of jeans. The cost of each shirt before the discount is 512 , and the cost of each pair of jeans is \( \$ 19 \) before the discount. a. Write and evaluate an expression to find the amount Pani pays if a \( \$ 3 \) discount is applied to her total. b. Pani says she should get a \( \$ 3 \) discount on the price of each shirt and a \( \$ 3 \) discount on the price of each pair of jeans. Write and evaluate an expression to find the amount she would pay if this is true. c. Analyze Relationships Why are the amounts Pani pays in a and b different?
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To find out how Pani’s discount scenario can affect her total bill, let’s break down the costs first! Pani is buying 3 shirts at $12 each and 2 pairs of jeans at $19 each. So, the total before discount is \( 3 \times 12 + 2 \times 19 = 36 + 38 = 74 \). With a flat $3 discount, Pani pays \( 74 - 3 = 71 \). Now, let's imagine Pani was right and those discounts applied individually! Each shirt would cost \( 12 - 3 = 9 \), and each pair of jeans would be \( 19 - 3 = 16 \). So, her new total would be \( 3 \times 9 + 2 \times 16 = 27 + 32 = 59 \). If Pani gets those separate discounts, she'd save even more! When discussing the differences between both scenarios: the first discount is applied to the total amount after adding together the costs of the shirts and jeans, which results in a lower overall discount. The second approach applies the discount to each item before calculating the total, which significantly reduces her bill! Pani’s perception of discounts can really affect her spending power!
