Chapter 8.5, Problem 46PPS

a.

To determine

To write a function that represents the number of songs the player can hold as a function of the average size of song.

Answer to Problem 46PPS

The required function is $5400=sn$

Explanation of Solution

Given information:

Total storage space of player is 5400 megabytes.

Consider s be the average size of song in megabytes and n be the number of songs.

As the total storage space of player can be represented as the product of average size of songs and number of songs.

The required function is $5400=sn$

b.

To determine

To write is the function a direct, joint, inverse, or combined variation.

Answer to Problem 46PPS

The function is inverse variation.

Explanation of Solution

Given information:

The equation is $5400=sn$

Write the standard form of the equation

  $\frac{5400}{n}=s$

There are two variables in the equation s and n . the equation is $y=\frac{k}{x}$ type where $k=5400$ , hence the equation represents inverse variation with constant of variation equals to 5400.

c.

To determine

To calculate how many more songs the player can hold if they are low quality than if they are high quality.

Answer to Problem 46PPS

The player can hold 405 five song more song if they are low quality than if they are high quality.

Explanation of Solution

Given information:

Average size for high quality songs is 8 megabytes and average size for low quality song is 5 megabyte.

Calculation:

Total number of high quality song player can hold

  $\begin{array}{l}5400=sn\\ n=\frac{5400}{s}\left[\text{divide each side by }s\right]\\ n=\frac{5400}{8}\left[\text{substitute value of }s\text{ for high quality song}\right]\\ n=675\end{array}$

Total number of low quality song player can hold

  $\begin{array}{l}5400=sn\\ n=\frac{5400}{s}\left[\text{divide each side by }s\right]\\ n=\frac{5400}{5}\left[\text{substitute value of }s\text{ for low quality song}\right]\\ n=1080\end{array}$

The difference in number of song

  $\begin{array}{l}=1080-675\\ =405\end{array}$

Therefore,

The player can hold 405 five song more song if they are low quality than if they are high quality.