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Let x be the number of days it would take for the two songs to have the same number of listens.
The equation for the first song would be:
1000 + 38x
The equation for the second song would be:
900 + 40x
Setting the two equations equal to each other, we have:
1000 + 38x = 900 + 40x
Solving for x:
1000 - 900 = 40x - 38x
100 = 2x
x = 50
Therefore, it would take 50 days for the two songs to have the same number of listens.