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.
-
Calculating the cost per song for 11 songs:
\[ \text{Cost per song} = \frac{5.83}{11} \approx 0.530 \]
-
Calculating the cost per song for 16 songs:
\[ \text{Cost per song} = \frac{8.48}{16} = 0.53 \]
-
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.
1 answer