Question
The table below shows the cost of downloading songs from a website.
Number of SongsNumber of Songs Total CostTotal Cost
1111 dollar sign, 5, point, 8, 3$5.83
1616 dollar sign, 8, point, 4, 8$8.48
1919 dollar sign, 10, point, 0, 7$10.07
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.
Number of SongsNumber of Songs Total CostTotal Cost
1111 dollar sign, 5, point, 8, 3$5.83
1616 dollar sign, 8, point, 4, 8$8.48
1919 dollar sign, 10, point, 0, 7$10.07
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.
Answers
GPT-4o mini
To find a proportional equation that represents the total cost \( c \) in terms of the number of songs downloaded \( s \), we start by observing the relationship between the number of songs and the total cost from the given data.
Based on the data you provided:
- For 11 songs, the cost is $5.83.
- For 16 songs, the cost is $8.48.
- For 19 songs, the cost is $10.07.
To find the unit cost (cost per song), we can use one or more of the data points.
1. **Calculating the cost per song for 11 songs:**
\[
\text{Cost per song} = \frac{5.83}{11} \approx 0.530
\]
2. **Calculating the cost per song for 16 songs:**
\[
\text{Cost per song} = \frac{8.48}{16} = 0.53
\]
3. **Calculating the cost per song for 19 songs:**
\[
\text{Cost per song} = \frac{10.07}{19} \approx 0.53
\]
Now we can see that the cost per song is consistent around $0.53. Since we have a consistent value, we can use it to write an equation.
Let \( c \) be the total cost in dollars and cents and \( s \) be the number of songs downloaded.
The proportional equation representing the total cost in terms of the number of songs can be written as:
\[
c = 0.53s
\]
This equation means that the total cost \( c \) is equal to $0.53 multiplied by the number of songs \( s \) downloaded.
Based on the data you provided:
- For 11 songs, the cost is $5.83.
- For 16 songs, the cost is $8.48.
- For 19 songs, the cost is $10.07.
To find the unit cost (cost per song), we can use one or more of the data points.
1. **Calculating the cost per song for 11 songs:**
\[
\text{Cost per song} = \frac{5.83}{11} \approx 0.530
\]
2. **Calculating the cost per song for 16 songs:**
\[
\text{Cost per song} = \frac{8.48}{16} = 0.53
\]
3. **Calculating the cost per song for 19 songs:**
\[
\text{Cost per song} = \frac{10.07}{19} \approx 0.53
\]
Now we can see that the cost per song is consistent around $0.53. Since we have a consistent value, we can use it to write an equation.
Let \( c \) be the total cost in dollars and cents and \( s \) be the number of songs downloaded.
The proportional equation representing the total cost in terms of the number of songs can be written as:
\[
c = 0.53s
\]
This equation means that the total cost \( c \) is equal to $0.53 multiplied by the number of songs \( s \) downloaded.