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) The songs will have the same number of listens after ___ days.

Answer 1

Let's denote the number of days after the start of the month as \( x \).

For the first song, the number of listens after \( x \) days can be expressed as:

\[
700 + 52x
\]

For the second song, the number of listens after \( x \) days can be expressed as:

\[
600 + 56x
\]

We want to find when both songs will have the same number of listens, so we set the two expressions equal to each other:

\[
700 + 52x = 600 + 56x
\]

Now, let's solve for \( x \):

1. First, subtract \( 52x \) from both sides:

\[
700 = 600 + 4x
\]

2. Next, subtract 600 from both sides:

\[
100 = 4x
\]

3. Finally, divide both sides by 4:

\[
x = 25
\]

Thus, the two songs will have the same number of listens after \( \boxed{25} \) days.