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To find out how many days it will take for the two songs to have the same number of listens, we can set up equations for the number of listens as a function of days.
Let \( x \) be the number of days.
For the first song:
- Initial listens: 1000
- New listens per day: 38
The equation for the number of listens for the first song after \( x \) days is:
\[ 1000 + 38x \]
For the second song:
- Initial listens: 900
- New listens per day: 40
The equation for the number of listens for the second song after \( x \) days is:
\[ 900 + 40x \]
To find the number of days it takes for the two songs to have the same number of listens:
Set the two equations equal to each other:
\[ 1000 + 38x = 900 + 40x \]
This equation can be solved for \( x \) to find the number of days.