# The formula for the number of seats sold in the flights.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.7, Problem 111E

(a)

To determine

## The formula for the number of seats sold in the flights.

Expert Solution

The formula for number of seat is 13P+5603_.

### Explanation of Solution

Given:

The number of seats sold at ticket price of $200 is 120. When the price of seat is increased by$3 , the number of seats sold decrease by one.

Calculation:

In the linear model f(P)=aP+b, let f(P) denote number of seats sold for price P dollars.

Since the number of seats sold at ticket price of $200 is 120, the linear model will be of with f(P)=120 and P=200. That is, 120=200a+b. When the price of seat is increased by$3, the number of seats sold decrease by one. That is, when price is P=200+(1×3) the number of seats becomes 119. That is, 119=203a+b

Equating 120=200a+b and 119=203a+b as follows:

120=200a+b119=203a+b_1=3aa=13

Substitute a=13 in 120=200a+b and obtain b as follows:

120=200(13)+b360+2003=bb=5603

Substitute a=13 and b=5603 in f(P)=aP+b to obtain the formula for the number of seats:

f(P)=13P+5603

So, the formula for the number of seats is 13P+5603_.

(b)

To determine

### The range of ticket prices for the given number of seats.

Expert Solution

The range for the ticket prices is from $215_ to$290_.

### Explanation of Solution

Given:

The number of seat sold for this flight range is 90 to 115.

Calculation:

From part (a), The formula for ticket price is f(P)=13P+5603.

Substitute the value 90 for f(P) in the f(P)=13P+5603.

90=13P+5603270=P+560P=560270P=$290 Substitute the value 115 for f(P) in the f(P)=13P+5603. 115=13P+5603345=P+560P=560345P=$215

Therefore, the range for the ticket prices is from $215_ to$290_.

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