Aaron is staying at a hotel that charges $100 per night plus tax for a room. A tax of 8% is applied to the room rate per day and an additional one-time only fee of $5.00 is charged by the hotel. Which of the following represents total charge, in dollars, for staying x nights?

A. left parenthesis 99.5 plus 0.08 x right parenthesis plus 5.

B. 1.08 open parentheses 99.95 x close parentheses plus 5.

C. 1.08 open parentheses 99.95 x plus 5 close parentheses.

D. 1.08 open parentheses 99.95 plus 5 close parentheses x.

B) 1.08 (99.95x) + 5

Step-by-step explanation:

Charges per night at the hotel = $ 100

Tax applied on room rate = 8%

One-time fee = $ 5

Since the tax is being applied on room rate, tax will be calculated on $ 100 only, not on $ 5.

Amount of tax = 8% of 100 = 0.08 x 100 = $ 8

After the tax, the charges per night for the stay at hotel would be = $ 108

Since $ 108 is being charged for one night, for x night the charges would be = $ 108 x

Total charge for staying x nights = Room charges + One time Fee

So,

Total charge for staying x nights = 108x + 5

This can also be written as:

Total charge for staying x nights = 1.08 (100x) + 5

This is because 108 = 1.08 x 100

By looking at the given options, option B gives the only possible answer.

Option B) 1.08 (99.95x) + 5

which simplifies to

1.08 (99.95x) + 5 = 107.946x + 5 ≈ 108x + 5

So, the correct answer for this question is B) 1.08 (99.95x) + 5