Question

At the beginning of the month, a song on a streaming service had 700 listens, and it was getting 52 new listens each day. Meanwhile, a different song had 600 listens, and it was getting 56 new listens each day. When will the two songs have the same number of listens? (1 point)

Answer 1

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 \( x \).

1. Subtract \( 52x \) from both sides:
\[
700 = 600 + 4x
\]

2. Subtract 600 from both sides:
\[
100 = 4x
\]

3. Divide both sides by 4:
\[
x = 25
\]

So, the two songs will have the same number of listens in **25 days**.