Let \( x \) represent the number of days that pass.
We can set up equations for the total listens for each song after \( x \) days.
For the first song: \[ \text{Total listens} = 700 + 52x \]
For the second song: \[ \text{Total listens} = 600 + 56x \]
We want to find the value of \( x \) when the two songs have the same number of listens, so we set the two equations equal to each other: \[ 700 + 52x = 600 + 56x \]
Now, we will solve for \( x \).
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Subtract \( 52x \) from both sides: \[ 700 = 600 + 4x \]
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Subtract 600 from both sides: \[ 100 = 4x \]
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Divide both sides by 4: \[ x = 25 \]
So, the two songs will have the same number of listens in 25 days.