Question

During an electronic store's Sale Days, the regular price of CD Players is discounted $10. There is a state sales tax of 5%, and the $10 discount is applied before the sales tax is calculated.

A. Write an expression that shows the regular price r of a CD Player minus the $10 discount.
B. Write a rule for the function p(r) that expresses the final price p of a CD Player with the discount applied and sales tax included
C. How much would you pay during Sale Days for a CD Player regularly priced at $29.50?

Answer 1

A) r - 10

B) p(r) = 1.05(r - 10)

C) $20.48 (nearest cent)

Explanation:

Part A

If r is the regular price of a CD player, then an expression for the regular price minus the $10 discount is:

• r - 10

Part B

If a state tax of 5% is applied to a sale, then the cost of the item will be 105% of its regular price. 105% expressed as a decimal is 1.05.

Therefore, we need to multiply the expression from part A by 1.05 to find the final price of the CD player:

• p(r) = 1.05(r - 10)

Part C

To calculate how much would you pay during Sale Days for a CD Player regularly priced at $29.50, substitute r = 29.5 into the function from part B:

⇒ p(r) = 1.05(29.50 - 10)

⇒ p(r) = 1.05(19.50)

⇒ p(r) = 20.475

Therefore, you would pay $20.48 (rounded to the nearest cent) for a CD Player during Sale Days.