Question

You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $95.00, two for $92.00 each, and in general the group rate per room is found by taking $3 off the base of $95 for each extra room rented. (a) How much money do you charge per room if a group rents 3 rooms? What is the total amount of money you take in? (b) Use a formula to give the rate you charge for each room if you rent n rooms to an organization. (c) Find a formula for a function R = R(n) that gives the total revenue from renting n rooms to a convention host. R(n) = (d) Use functional notation to show the total revenue from renting a block of 7 rooms to a group. Calculate the value. R( )=$

          You own a motel with 30 rooms and have a pricing structure that
encourages rentals of rooms in groups. One room rents
for $95.00, two for $92.00 each, and in general the
group rate per room is found by taking $3 off the base
of $95 for each extra room rented.
(a) How much money do you charge per room if a group rents 3
rooms?
  What is the total amount of money you take in?
(b) Use a formula to give the rate you charge for each room if you
rent n rooms to an organization.
 (c) Find a formula for a
function R = R(n) that
gives the total revenue from renting n rooms to
a convention host.
R(n) = 
(d) Use functional notation to show the total revenue from renting
a block of 7 rooms to a group. Calculate the value.
R( )=$

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Added by Emilia G.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Supreeta N

09/07/2023

Step 1

Since there are 2 extra rooms, we take $3 * 2 = $6 off the base price. So, the rate per room for 3 rooms is $95 - $6 = $89. The total amount of money you take in for 3 rooms is $89 * 3 = $267. (b) Show more…

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You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $95.00, two for $92.00 each, and in general the group rate per room is found by taking $3 off the base of $95 for each extra room rented. (a) How much money do you charge per room if a group rents 3 rooms? What is the total amount of money you take in? (b) Use a formula to give the rate you charge for each room if you rent n rooms to an organization. (c) Find a formula for a function R = R(n) that gives the total revenue from renting n rooms to a convention host. R(n) = (d) Use functional notation to show the total revenue from renting a block of 7 rooms to a group. Calculate the value. R( )=$

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00:02 Hello, we have a motel which has 30 rooms.

00:07 So, the total number of rooms is given to be 30.

00:18 And the pricing structure for renting the rooms is one room is rented at $95 per room and two rooms are rented in a block.

00:39 That is two rooms together are rented at $92 per room.

00:48 In general, if we are renting out a block of n rooms, the price per room is 95 minus three times the number of additional rooms.

01:08 For example, in a block of n rooms, we are renting out n minus one additional rooms.

01:14 So, the price per room will be 95 minus three times the number of additional rooms which is n minus one.

01:27 This will be the price per room.

01:30 This is the price per room.

01:36 If n rooms are rented in a block, then the price per room is 95 minus three times n minus one dollars.

01:48 Okay, the first question we are asked is, if three rooms are rented to a group in a block, what is the price per room? so, three room block, for this three room block, the price per room is 95 minus, we can use this formula, 95 minus three times n minus one is two here, which is equal to per room, this is equal to dollars.

02:36 Three times two is six.

02:39 95 minus six is 89.

02:42 So, it is $89 per room.

02:47 And we also have to find what is the total revenue or what is the total money we get by renting the three room block.

02:57 Total money we take in from the block of three rooms is equal to three times $89, which is equal to $267...

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