Chapter 4.3, Problem 35PPS

To determine

To find: The number of copies rented during the second week.

Answer to Problem 35PPS

The number of copies rented during the second week are 24.

Explanation of Solution

Given information: The number of copies of a movie rented at a video store decreased at a constant rate of 5 copies per week. And, after 6^th week 4 copies were rented.

Considering that the number of copies rented are $\left(y\right)$ , number of initial copies are $\left(i\right)$ and number of weeks are $\left(x\right)$ .

Calculation: According to question, the number of copies rented $\left(y\right)$ = number of initial copies $\left(i\right)$ minus 5 times the number of weeks $\left(x\right)$ .

  $y=i-\left(5\right)\left(x\right)\mathrm{......}\left(1\right)$

Now, for 6^th week, the number of copies rented are 4, according to question. Therefore, plugging $x=6$ and $y=4$ in (1) gives the number of initial copies $\left(i\right)$ ,

  $\begin{array}{c}4=i-\left(5\right)\left(6\right)\\ \text{or, }i=4+30\\ i=34\end{array}$

Plugging $i=34$ in (1),

  $\begin{array}{l}y=\left(34\right)-\left(5\right)\left(x\right)\\ y=-5x+\mathrm{34......}\left(2\right)\end{array}$

For, second week the number of copies rented are calculated by plugging $x=2$ in (2),

  $\begin{array}{l}y=-5\left(2\right)+\mathrm{34......}\left({\text{For 2}}^{nd}\text{ week }x=2\right)\\ y=24\end{array}$

Hence, the number of copies rented during the second week are 24.