Question

A resort hotel charges 12.5% in taxes. Additionally they charge a $25 resort fee each day. (The resort fee is not subject to sales tax.)

The following functions represents the situation:
f (a) = 1.125a
g (b) = b + 25

a. Match the following to their description
1. ___ a A. The cost of the hotel room and sales tax, but without the resort fee
2. ___ b B. The cost of the hotel room without sales tax or the resort fee.
3. ___ f (a) C. The cost of the hotel room, with sales tax and the resort fee.
4. ___ g (b)

Answer 1

We know that the hotel charges 12.5% in taxes (or 0.125 in decimal form).

Then if the initial cost of the hotel, without taxes, is a, the price with taxes will be:

f(a) = a + 0.125*a = 1.125*a

And the hotel also charges a fee of $25 for each day (that is not subject to taxes) then if the total cost, with taxes, is b, the actual cost will be:

g(b) = b + 25.

Then:

a = The cost of the hotel room without sales tax or the resort fee.

f(a) and b= The cost of the hotel room and sales tax, but without the resort fee

g(b) = The cost of the hotel room, with sales tax and the resort fee.