Chapter 8.1, Problem 49STP

(a)

To determine

To calculate: To write an equation that gives the total cost as a function of the number of songs downloaded.

Answer to Problem 49STP

The equation that gives the total cost as a function of the number of songs downloaded is $y=1.75x+15$

Explanation of Solution

Given information: For song downloads, K pays $\$15$ per month plus $\$1.75$ per song

Calculation:

Given that for song downloads, K pays $\$15$ per month plus $\$1.75$ per song

Let us assume that total cost be $y$ and cost of per song be $x$

Thus, equation is given as

  $y=1.75x+15$

Conclusion:

Hence, required equation is $y=1.75x+15$

(b)

To determine

To calculate: To find how much would K’s total bill if she downloaded $15$ songs

Answer to Problem 49STP

The cost of downloading $15$ songs is $\$41.25$

Explanation of Solution

Given information: For song downloads, K pays $\$15$ per month plus $\$1.75$ per song

Calculation:

Given that for song downloads, K pays $\$15$ per month plus $\$1.75$ per song

Let us assume that total cost be $y$ and cost of per song be $x$

Thus, equation is given as

  $y=1.75x+15$

Cost of downloading $15$ is calculated by substituting $x=15$ in above equation

  $\begin{array}{l}y=1.75\left(15\right)+15\\ y=26.25+15\\ y=41.25\end{array}$

Conclusion:

Hence, the cost of downloading $15$ songs is $\$41.25$

(c)

To determine

To calculate: To make a function table to show K’s total bill if she downloaded $15,20,25,30$ songs

Answer to Problem 49STP

Table is

Number of songs downloaded	Total Cost
15	41.25
20	50
25	58.75
30	67.5

Explanation of Solution

Given information: For song downloads, K pays $\$15$ per month plus $\$1.75$ per song

Calculation:

Given that for song downloads, K pays $\$15$ per month plus $\$1.75$ per song

Let us assume that total cost be $y$ and cost of per song be $x$

Thus, equation is given as

  $y=1.75x+15$

When $x=15$

  $\begin{array}{l}y=1.75\left(15\right)+15\\ y=26.25+15\\ y=41.25\end{array}$

When $x=20$

  $\begin{array}{l}y=1.75\left(20\right)+15\\ y=35+15\\ y=50\end{array}$

When $x=25$

  $\begin{array}{l}y=1.75\left(25\right)+15\\ y=43.75+15\\ y=58.75\end{array}$

When $x=30$

  $\begin{array}{l}y=1.75\left(30\right)+15\\ y=52.5+15\\ y=67.5\end{array}$

Thus, table is

Number of songs downloaded	Total Cost
15	41.25
20	50
25	58.75
30	67.5

Conclusion:

Hence, the table is created