Question

Luis bought a smartwatch at a store that gave a 15 percent student discount off its original price. He paid the cashier d dollars, including a 7% sales tax on the discounted price. Write an equation that represents the original price of the smartwatch in terms of d.

A) Original Price = 1.07d / 0.85
B) Original Price = 0.85d / 1.07
C) Original Price = 0.85d / 1.07
D) Original Price = 1.07d / 0.85

Answer 1

The equation that represents the original price of the smartwatch in terms of d is Original Price = d / 0.9115.

Step-by-step explanation:

Let's break down the problem step-by-step.

Step 1: Apply the student discount

Luis received a 15 percent student discount on the original price of the smartwatch. This means he paid 85% of the original price:

Discounted Price = 0.85 * Original Price

Step 2: Calculate the total cost including sales tax

Luis paid the cashier d dollars, including a 7% sales tax on the discounted price. This can be represented as:

Total Cost = Discounted Price + (0.07 * Discounted Price)

Total Cost = 1.07 * Discounted Price

Step 3: Substitute the value of Discounted Price

From Step 1, we know that the Discounted Price is 0.85 times the Original Price. Substituting this value in the equation from Step 2, we get:

Total Cost = 1.07 * (0.85 * Original Price)

Simplifying the equation, we find:

Total Cost = 0.9115 * Original Price

Step 4: Solve for Original Price

To find the Original Price in terms of d, we divide both sides of the equation by 0.9115:

Original Price = Total Cost / 0.9115

Original Price = d / 0.9115

Therefore, the equation that represents the original price of the smartwatch in terms of d is Original Price = d / 0.9115.