label Mathematics
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ou own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for \$80.00, two for \$78.00 each, and in general the group rate per room is found by taking \$2 off the base of \$80 for each extra room rented.

(a) How much money do you charge per room if a group rents 3 rooms?

What is the total amount of money you take in?

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

(c) Find a formula for a function R = R(n) that gives the total revenue from renting n rooms to a convention host.
R(n) =

Sep 10th, 2015

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

(a) : = \$76     total amount = 80+78+76 =  \$ 234

(b) formula Rent  = 80-2 (n-1)   where n is the number of room rented...

solving we get Rent   = 80-2n+2  hence Formula is Rent   = 82-2n

(c)  revenue : 80 + 80-2*(1)+ 80-2*(2)  + -------- 80 -2*(n-1)

hence we can write : 80n -2*[ 1+2+3 + ----- (n-1)]

or ,  80n -2 *(n-1)(n)/2  = 80n -n(n-1)

or 80n-n^2+n   = 81n-n^2

hence Revenue R(n) = 81n-n^2

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Sep 10th, 2015

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Sep 10th, 2015
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Sep 10th, 2015
Oct 19th, 2017
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