Question

14. Hotel Rates You rent a hotel room for $72 a night. The hotel adds a charge for using its parking lot to the total bill, Afterstaying at the hotel for 3 nights, your total bill is $231.a. Write an equation in slope-intercept form that gives your total bill (in dollars) as a function of the number ofnights you stay in the room.b. How much of your bill was for the parking fee?c.How much does it cost to stay at the hotel for 7 nights?d. If your bill was $591, how many nights did you stay at the hotel?

Answer 1

(a)y=72x+15

(b)$15

(c)519

(d)8 nights

Step-by-step explanation:

Let the number of nights which you stay = x

The cost of renting a room for a night =$72

Therefore, the costs for x nights = $72x

If the charge for using its parking lot = c

Then, the total cost, y=72x+c

Part A

When the total bill = $231

x=3 nights

`\begin{gathered} 231=72(3)+c \\ 231=216+c \\ c=231-216 \\ c=15 \end{gathered}`

Therefore, an equation in slope-intercept form that gives your total bill as a function of the number of nights, x is:

`y=72x+15`

Part B

Your packing fee, c=$15

Part C

When the number of nights, x=7

`\begin{gathered} \text{Total Cost,y}=72(7)+15 \\ =504+15 \\ =\$519 \end{gathered}`

Part D

When the total cost, y = $591

`\begin{gathered} 591=72x+15 \\ 72x=591-15 \\ 72x=576 \\ (72x)/(72)=(576)/(72) \\ x=8 \end{gathered}`

If your bill was $591, you stayed for 8 nights.