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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 blank days.

1 answer

Let's denote the number of listens for the first song as \( L_1 \) and for the second song as \( L_2 \).

Initially:

  • The first song has 700 listens and gains 52 listens per day.
  • The second song has 600 listens and gains 56 listens per day.

The number of listens for each song after \( x \) days can be expressed as:

  • For the first song: \( L_1 = 700 + 52x \)
  • For the second song: \( L_2 = 600 + 56x \)

We want to find \( x \) when \( L_1 = L_2 \). Thus, we set up the equation:

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

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

  1. Subtract \( 52x \) from both sides:

\[ 700 = 600 + 4x \]

  1. Subtract 600 from both sides:

\[ 100 = 4x \]

  1. Divide both sides by 4:

\[ x = 25 \]

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