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What is the constant of proportionality between the total cost and the number 

To find the constant of proportionality between the total cost and the number of songs, we can use the formula:

\[
k = \frac{\text{Total Cost}}{\text{Number of Songs}}
\]

We'll calculate this for each pair of values from the table:

- For 3 songs:  
\[
k = \frac{1.14}{3} = 0.38
\]

- For 12 songs:  
\[
k = \frac{4.56}{12} = 0.38
\]

- For 16 songs:  
\[
k = \frac{6.08}{16} = 0.38
\]

The constant of proportionality $ k $ is $ 0.38 $. This means that each song costs approximately **$0.38**.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. How would you write an equation to represent the total cost as a function of the number of songs?
2. If the cost per song increased to $0.50, what would the total cost be for downloading 20 songs?
3. If you have $10, how many songs can you download at the current rate?
4. What is the total cost for downloading 25 songs using the constant of proportionality found?
5. How does the concept of proportionality help in solving real-world problems?

**Tip**: Always check if a relationship is proportional by ensuring the ratio remains constant across different data points.

What is the constant of proportionality between the total cost and the number of songs?

Learn how to find the constant of proportionality between the total cost and the number of songs downloaded. This problem involves calculating the ratio between cost and quantity to determine a consistent price per song.

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