Question

The table below shows the cost of downloading songs from a website. Number of Songs Total Cost 14 $8.96 16 $10.24 18 $11.52 If c represents the total cost in dollars and cents for any number of songs downloaded, s, write a proportional equation for c in terms of s that matches the S, context.

Answer 1

Given:

c = total cost.

s = number of songs.

To solve this question, follow the steps below.

Step 01: Find 2 points (s, c).

You can choose 2 points from the table.

Let's choose (14, 8.96) and (16, 10.24).

Step 02: Substitute one point in the general equation.

Given the general equation:

$c=ms+b$

Substituting the first point.

$\begin{gathered} 8.96=14m+b \\ 8.96-14m=b \\ b=8.96-14m \end{gathered}$

Isolating b by subtracting 8.96 m from both sides:

$\begin{gathered} 14-8.96m=8.96m+b-8.96m \\ 14-8.96m=b \\ b=14-8.96m \end{gathered}$

Step 03: Substitute b in the general equation.

$\begin{gathered} c=ms+b \\ c=ms+8.96-14m \end{gathered}$

Step 04: Substitute the second point in the equation above.

$\begin{gathered} c=ms+8.96-14m \\ 10.24=16m+8.96-14m \\ 10.24=2m+8.96 \end{gathered}$

Step 05: Solve the equation above for m.

To do it, first, subtract 8.96 from both sides.

$\begin{gathered} 10.24-8.96=2m+8.96-8.96 \\ 1.28=2m \end{gathered}$

Now, divide both sides by 2.

$\begin{gathered} \frac{1.28}{2}=\frac{2}{2}m \\ m=0.64 \end{gathered}$

Step 06: Substitute m in the equation from step 02 to find b.

$\begin{gathered} b=8.96-14m \\ b=8.96-14\cdot0.64 \\ b=8.96-8.96 \\ b=0 \end{gathered}$

Step 07: Write the equation.

$\begin{gathered} c=0.64s+0 \\ c=0.64s \end{gathered}$

Answer:

c = 0.64s