Can someone please help me understand ?

label Mathematics
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You own a motel with 46 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $70, two rent for $67 each, and in general the group rate per room is found by taking $3 off the base of $70 for each extra room rented.

(a) How much money do you take in if a family rents four rooms? (Round your answer to the nearest dollar.)

(b) Use a formula to give the rate you charge for each room if you rent n rooms to an organization. 

Oct 3rd, 2015

Thank you for the opportunity to help you with your question!

As described in the problem, for each extra room rented there will be $3 off the base price of 70$

(a) Now, when a family rents four rooms.  That means they have rented 3 extra rooms.

$3 off for each extra room so discount for 3 extra rooms =  3 * 3$ = 9$

So price per each room is base price -  discount i.e. 70$ - 9$ = 61$

Price for four rooms = 4 * 61$ = 244$

(b)  Formula for computing rate you charge for one room when n rooms are rented is:

       Rate per room = 70$ - ( (n-1) * 3$)

       Above formula can be solved to get  73$ - 3n$

      Above formula is derived using below logic

     Rate per room = Base Price - (Number of extra rooms * 3$)

Note: In case you are asked to find out total price for n rooms, then you need to multiply price per room with n.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 21st, 2015

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