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?
the songs will have the same number of listens after ___ days

Answer 1

Let \( x \) represent the number of days after the beginning of the month.

For the first song, we can express the number of listens after \( x \) days as:
\[
700 + 52x
\]

For the second song, we can express the number of listens after \( x \) days as:
\[
600 + 56x
\]

We need to find the value of \( x \) when both songs have the same number of listens:
\[
700 + 52x = 600 + 56x
\]

Now, let's 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:
\[
x = 25
\]

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