
Concept explainers
(a).
Write two functions representing the price after the discount p(x) and the price after sales tax t(x).
(a).

Answer to Problem 37PPS
Explanation of Solution
Given:
Ms.Smith wants to buy an HDTV , which is on sale for 35% off the original price of $2299.The sales tax is 6.25%.
Calculation:
Let the original price of the HDTV = x
Discount = 35%
So, the price after discount = original price − discount =
So, the function for the price after discount :
Sales tax rate = 6.25%
So, the price after sales tax is added to it = original price + sales tax =
So, the function for the price after sales tax :
(b).
Find the composition of functions that represents the price of the HDTV ,
(b).

Answer to Problem 37PPS
Explanation of Solution
Given:
Ms.Smith wants to buy an HDTV , which is on sale for 35% off the original price of $2299.The sales tax is 6.25%.
Calculation:
From part (a) , we have:
The function for the price after discount :
The function for the price after sales tax :
Since, Ms.Smith pays sales tax on the discounted price of the HDTV, we need to first apply the function that gives the price of HDTV after the discount of 35% and then apply the function that applies the sales tax on the discounted price of the HDTV.
Hence, the correct composition is :
So,
(c).
Find the price that Ms. Smith will pay for the HDTV.
(c).

Answer to Problem 37PPS
The price of HDTV after the discount and the sales tax is approximately $1587.75
Explanation of Solution
Given:
Ms.Smith wants to buy an HDTV , which is on sale for 35% off the original price of $2299.The sales tax is 6.25%.
Calculation:
From part (a) , we have:
The function for the price after discount :
The function for the price after sales tax :
and from part (b) , we have:
We have , x = $2299
So, the price of HDTV after the discount and the sales tax is approximately $1587.75
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