The owner of a motel has 60 rooms to rent. She finds that if she charges $20 per room per night, all the roomswill be rented. For ever $2 that she increases the price of a room, three rooms will stand vacant.a. Complete the table.# of price# of roomsPriceTotal revenueincreasementsrented20601200225712542347.8.10121620b. Let z stand for the number of $2 price increases the owners make. Write algebrais expressions for the price ofa room, the number of rooms that will be rented, and the total revenue carned at that price.Price of a room:PreviewNumber of rooms rented:PreviewTotal revenue:Preview Number of rooms rented:PreviewTotal revenue:Previewc. Use your calculator to make a table of values for your algebraic expressions. Let Y stand for the price of aroom, Y, for the number of rooms rented, and Y3 for the total revenue. Verify the values you calculated in part a.d. Use your table to find a value of æ that causes the total revenue to be zero.e. Use your graphing calculator to graph your formula for total revenue.f. What is the lowest price that the owner can charge for a room if she wants her revenue to exceed $1296 pernight?2$What is the highest price she can charge to obtain this revenue?g. What is the maximum revenue the owner can earn in one night?How much should she charge for a room to maximize her revenue?How many rooms will she rent at that price?

Note there are many subparts in question. So I will answer the first two of them and other subparts,…

The owner of a motel has 60 rooms to rent. She finds that if she charges $20 per room per night, all the rooms will be rented. For ever $2 that she increases the price of a room, three rooms will stand vacant. a. Complete the table. # of price # of rooms Price Total revenue increasements rented 0. 20 60 1200 22 57 1254 3. 4. 8. 10 12 16 20 b. Let z stand for the number of $2 price increases the owners make. Write algebraid expressions for the price of a room, the number of rooms that will be rented, and the total revenue carned at that price. Price of a room: Preview Number of rooms rented: Preview Total revenue: Preview

The owner of a motel has 60 rooms to rent. She finds that if she charges $20 per room per night, all the rooms will be rented. For ever $2 that she increases the price of a room, three rooms will stand vacant. a. Complete the table. # of price # of rooms Price Total revenue increasements rented 0. 20 60 1200 22 57 1254 3. 4. 8. 10 12 16 20 b. Let z stand for the number of $2 price increases the owners make. Write algebraid expressions for the price of a room, the number of rooms that will be rented, and the total revenue carned at that price. Price of a room: Preview Number of rooms rented: Preview Total revenue: Preview

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

The owner of a motel has 60 rooms to rent. She finds that if she charges $20 per room per night, all the rooms
will be rented. For ever $2 that she increases the price of a room, three rooms will stand vacant.
a. Complete the table.
# of price
# of rooms
Price
Total revenue
increasements
rented
20
60
1200
22
57
1254
2
3
4
7.
8.
10
12
16
20
b. Let z stand for the number of $2 price increases the owners make. Write algebrais expressions for the price of
a room, the number of rooms that will be rented, and the total revenue carned at that price.
Price of a room:
Preview
Number of rooms rented:
Preview
Total revenue:
Preview

Number of rooms rented:
Preview
Total revenue:
Preview
c. Use your calculator to make a table of values for your algebraic expressions. Let Y stand for the price of a
room, Y, for the number of rooms rented, and Y3 for the total revenue. Verify the values you calculated in part a.
d. Use your table to find a value of æ that causes the total revenue to be zero.
e. Use your graphing calculator to graph your formula for total revenue.
f. What is the lowest price that the owner can charge for a room if she wants her revenue to exceed $1296 per
night?
2$
What is the highest price she can charge to obtain this revenue?
g. What is the maximum revenue the owner can earn in one night?
How much should she charge for a room to maximize her revenue?
How many rooms will she rent at that price?

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