Let's break down and answer your question step by step:
### Part A: Sale of the song
First, let's analyze the given expression. Unfortunately, the notation and arrangement in the question are quite unclear. However, the final simplified ratio given is [tex]\(5:1\)[/tex]. So, to be clear:
[tex]\[
\frac{\left(200, \frac{40}{40}\right.}{40}\left(\frac{1000}{120} \frac{120}{12}\right) = 5:1
\][/tex]
This indicates that the ratio between the dollars earned and song sales is [tex]\(5:1\)[/tex]. For every song sold, the pop star earns 5 dollars.
### Part B: Write an equation to determine the money paid to the pop star
Based on the ratio given in Part A, we can write an equation for the money [tex]\(p\)[/tex] paid to the pop star in dollars, based on the sales of the song [tex]\(s\)[/tex]. Given that for each sale (1 song), the pop star earns [tex]$5, the equation can be written as:
\[
p = 5s
\]
### Part C: What does the equation indicate about the relationship between dollars earned and song sales?
The equation \( p = 5s \) indicates a direct proportional relationship between the dollars earned \( p \) and the song sales \( s \).
- For each song sold (s), the pop star earns 5 dollars (p).
- If the pop star sells 2 songs, they earn \( 5 \times 2 = 10 \) dollars.
- If they sell 10 songs, they earn \( 5 \times 10 = 50 \) dollars.
In conclusion, the relationship shows that the earnings increase linearly with each additional song sold. For every single song sale, the pop star's earnings increase by $[/tex]5.
This straightforward relationship is essential in understanding how the sales directly influence the payout to the pop star, showcasing a simple and proportional earning pattern.
