Question

Part 1 - Application

Indiana plans to purchase a new gaming system during the 15% off sale. Let c represent the cost of the gaming system. How can you write a function to represent this?


Indiana also knows that he will have to pay the state tax of 10% on his purchase (after the discount is taken). Let p represent the price. How can he write a function to represent this?


Write one single function to help Indiana know how to calculate the final cost.

Answer 1

The single function to calculate the final cost of the gaming system, including a 15% off discount and a 10% state tax, is: final_cost(c) = 0.935c.

Explanation:

To represent the cost of the gaming system before any discounts or taxes, we can use the variable c:

c represents the cost of the gaming system.

To represent the price after the 15% off discount, we need to calculate the discounted price by subtracting 15% of the cost from the original cost:

p = c - 0.15c

Simplifying, we get:

p = 0.85c

Here, p represents the price after the 15% discount has been applied.

To represent the price after the 10% state tax has been added to the discounted price, we need to calculate the price with the added tax:

final_price = p + 0.1p

Simplifying, we get:

final_price = 1.1p

Here, final_price represents the price after the 10% state tax has been added.

Therefore, the correct single function to help Indiana calculate the final cost is:

final_cost(c) = 1.1(0.85c)

Simplifying further:

final_cost(c) = 0.935c