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)

Question

The songs will have the same number of listens after___
days.

Answer 1

Let's denote the number of days after the beginning of the month as \( d \).

For the first song:

• Initial listens = 700
• New listens per day = 52
• Total listens after \( d \) days = \( 700 + 52d \)

For the second song:

• Initial listens = 600
• New listens per day = 56
• Total listens after \( d \) days = \( 600 + 56d \)

To find when the two songs have the same number of listens, we set up the equation:

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

Now, we can solve this equation for \( d \):

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

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

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

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