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?

Rationale

0.85x - 5 represents the final price the customer will pay for the shirt.

To find the price the customer pays after applying the discounts, first, the shirt's sale price is calculated at 85% of the original price (15% off), and then the $5 coupon is subtracted from that sale price.

A (0.15x-5) YOUR ANSWER

This option incorrectly represents the price by calculating 15% of the original price and then subtracting $5. Instead, we need to find 85% of the original price and then subtract the coupon amount.

B (0.85x -5) CORRECT

This is the correct choice. The expression represents the sale price of the shirt after a 15% discount (which is 85% of the original price, x) minus the $5 coupon. This accurately reflects the total amount the customer pays for the shirt.

C (0.85(x-5)) YOUR ANSWER

This choice suggests that the customer first reduces the original price by $5 and then takes 85% of that reduced price. However, the coupon should be applied after calculating the sale price, not before.

D (5-0.85x) YOUR ANSWER

This expression implies that the customer pays $5 minus 85% of the original price, which is nonsensical in this context. The customer cannot end up with a negative price, and the calculation does not account for the discounts properly.

Conclusion

The final price the customer pays for the shirt after a 15% discount and applying a $5 coupon is accurately expressed as 0.85x - 5. This formulation correctly reflects the sale price and the additional discount, ensuring clarity in the pricing structure.