At the beginning of each 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 listens for the first song as \( L_1 \) and for the second song as \( L_2 \).

1. The initial listens for the first song: \[ L_1 = 700 + 52d \] where \( d \) is the number of days since the beginning of the month.

2. The initial listens for the second song: \[ L_2 = 600 + 56d \]

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

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: \[ d = 25 \]

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