13. A shirt is on sale for 15 percent off the original price of x dollars. If a customer has a coupon for 5 dollars off the sale price, which of the following represents the price, in dollars, the customer will pay, excluding tax, for the shirt?
Answer: B
The price the customer will pay for the shirt is represented by 0.85x - 5.
To determine the final price the customer pays after applying the discount and coupon, we subtract 15 percent from the original price, resulting in 85 percent of the original price, and then deduct the additional 5 dollars from that sale price.
A) 0.15x-5
This option incorrectly represents the calculation by taking 15 percent of the original price and subtracting 5 dollars. Instead, the price should be calculated after applying the discount, not just using the discount percentage itself.
B) 0.85x -5
This option correctly represents the price the customer will pay. It calculates 85 percent of the original price (x), reflecting the 15 percent discount, and then subtracts the 5 dollars coupon, which accurately represents the final amount payable.
C) 0.85(x-5)
This option incorrectly suggests that the 5 dollars coupon is applied before calculating the 15 percent discount. The discount should first be applied to the original price, not to a reduced price, making this option incorrect.
D) 5-0.85x
This option incorrectly implies that the price the customer will pay is derived by subtracting 85 percent of the original price from 5 dollars. This does not accurately reflect the pricing structure after applying the discount and coupon, rendering it incorrect.
Conclusion
The correct answer, 0.85x - 5, accurately reflects the final price after a 15 percent discount is applied to the original price followed by a 5 dollar deduction from the sale price. All other options fail to represent the correct sequence of applying the discount and the coupon, leading to their incorrectness.