More 1.4 Problems
1. A party cruise can be booked for a flat fee of $1500 plus $350 per person. However, discounts
are given for larger groups. For each person in excess of 10 that is part of the group, the price
per person (for all people) decreases by $15. Let C x represent the total cost to book such a
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cruise when x people are in the group.
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(a) Find and interpret C 8 .
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(b) Find and interpret C 12 .
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(c) Find and interpret C 15 .
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(d) Give a simplified formula for C x .
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2. You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms
in groups. One room rents for $85 per night, two for $83 each per night, and in general the
group rate per room per night is found by taking $2 off the base $85 for each additional room
rented. Let R x, n be the money taken in when a group rents x rooms for n nights.
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(a) Find and interpret R 2, 3
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(b) Find and interpret R 4, 2
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(c) Give a simplified formula for R x, n
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Solutions
1. (a) price per person = $350, so cost = 1500 + 350(8) = $4300
The total cost if 8 people are in the group is $4300.
(b) price per person = 350 -15(2) = 320, so cost = 1500 + 320(12) = $5340
The total cost if 12 people are in the group is $5340
(c) price per person = 350 -15(5) = 275, so cost = 1500 + 275(15) = $5625
The total cost if 15 people are in the group is $5625
(d) If 10 or fewer people go, the price per person is $350 and the cost is 1500 + 350x.
If more than 10 people go, then the price per person is 350 – 15(x – 10).
In this cast the cost is 1500 + (350 – 15(x – 10))x. Simplifying this gives:
1500350x
x  10
C x  
2
1500500x  15x x  10
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2. (a) price per night = 85 – 2(1) = 83, so cost is 83(2)(3) = $498
The revenue from 2 rooms rented for 3 nights is $498.
(a) price per night = 85 – 2(3) = 79, so cost is 79(4)(2) = $632
The revenue from 4 rooms rented for 2 nights is $632.
(a) price per night = 85 – 2(x – 1) = 87 – 2x
So,
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R x, n  87 2x xn
 87xn 2x 2n
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