Chapter 6.5, Problem 21PPS

a.

To determine

To calculate the cost that music club charges to download a song.

Answer to Problem 21PPS

$2.43

Explanation of Solution

Given:

Kendrick pays $14.90 to download 5 individual songs and 1 album.

Geoffrey pays $12.75 to download 3 individual songs and 2 albums.

Calculation:

Let x be the cost of downloading an individual song and y be the cost of downloading an album.

Given that Kendrick pays $14.90 to download 5 individual songs and 1 album.

  $\Rightarrow 5x+y=\mathrm{14.90...................}(1)$

Also, Geoffrey pays $12.75 to download 3 individual songs and 2 albums.

  $\Rightarrow 3x+2y=\mathrm{12.75...................}(2)$

Multiply equation (1) with 2,

  $\Rightarrow 10x+2y=\mathrm{29.80................}(3)$

Subtract equation (2) from equation (3), so that y is eliminated.

  $\begin{array}{l}\Rightarrow (10x+2y)-(3x-2y)=29.80-12.75\\ \Rightarrow 7x=17.05\\ \Rightarrow x=2.43\end{array}$

Conclusion:

Therefore, the cost of downloading a song is $2.43.

b.

To determine

To calculate the cost that music club charges to download an entire album

Answer to Problem 21PPS

$2.75

Explanation of Solution

Given:

From subpart (a), x = 2.43

  $5x+y=14.90$

  $3x+2y=12.75$

Calculation:

Substitute the value of x in any one of the equations,

  $\begin{array}{c}5x+y=14.90\\ 5(2.43)+y=14.90\\ 12.15+y=14.90\\ y=2.75\end{array}$

Conclusion:

Therefore, the cost of downloading an album is $2.75.