Chapter 7.1, Problem 81E

To determine

To calculate the number of rentals of each movie for first 12 weeks from the following functions as:

  $N=360-24x\text{Animated}\text{film}$

  $N=24+18x\text{Horror}\text{film}$

Answer to Problem 81E

Thesolution of the given linear equations is $x=8$

Explanation of Solution

Given information: The given functions are:

  $\text{Animated}\text{film: }N=360-24x$

  $\text{Horror}\text{film: }N=24+18x$

Where, $N$ is the number of DVDs rented and $x$ is the week.

Calculation:

(a)  Using graphing utility to find the number of rentals for each movie is given in the following table:

Number of weeks =   $x$	$\begin{array}{l}\text{Animated}\text{film:}\\ N=360-24x\end{array}$	$\begin{array}{l}\text{Horror}\text{film}\\ N=24+18x\end{array}$
1	336	42
2	312	60
3	288	78
4	264	96
5	240	114
6	216	132
7	192	150
8	168	168
9	144	186
10	120	204
11	96	222
12	72	240

(b) From the above table, it is concluded that the number of rentals of each movie is

same at $x=8$

Hence, the solution of the given linear equations is $x=8$

(c) The given equations are:

  $N=360-24x;N=24+18x$

  $\Rightarrow 360-24x=24+18x$

  $\Rightarrow 42x=336$

  $\Rightarrow x=8$

Hence, the solution of the given linear equations is $x=8$

(d) From the part(b) and part(c), it is concluded that the solution of the algebraic equations is same.

(e) From the results, it has been found that in 8^th week, the demand of each type of movie is same.