The table below shows the cost of downloading songs from a website.

Question

Number of SongsNumber of Songs Total CostTotal Cost
1313 dollar sign, 8, point, 9, 7$8.97
1616 dollar sign, 11, point, 0, 4$11.04
1818 dollar sign, 12, point, 4, 2$12.42
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 context.

Answer 1

To determine a proportional equation for the total cost \( c \) in terms of the number of songs \( s \), we can analyze the data provided:

We have the following data points:

1. \( 13 \) songs for \( $8.97 \)
2. \( 16 \) songs for \( $11.04 \)
3. \( 18 \) songs for \( $12.42 \)

To find a proportional relationship, we can check if the total cost per song is consistent. We will calculate the cost per song for each data point.

1. For \( 13 \) songs: \[ \text{Cost per song} = \frac{8.97}{13} \approx 0.6923 \]

2. For \( 16 \) songs: \[ \text{Cost per song} = \frac{11.04}{16} = 0.690 \]

3. For \( 18 \) songs: \[ \text{Cost per song} = \frac{12.42}{18} \approx 0.6911 \]

The cost per song is around \( 0.69 \). To establish a proportional relationship, we can use the average cost per song as the rate.

Let's take the average cost per song: \[ \text{Average cost per song} \approx 0.691 \text{ (we can round this to } 0.69\text{ for simplicity)} \]

Now we can set up a proportional equation for the total cost \( c \) in terms of the number of songs \( s \): \[ c = 0.69s \]

This equation reflects that the total cost \( c \) in dollars is approximately \( 0.69 \) times the number of songs \( s \) downloaded. Thus, the proportional equation is: \[ c = 0.69s \]