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?

Question

(1 point)
The songs will have the same number
of listens after days.

Answer 1

To find out when the two songs will have the same number of listens, we can set up an equation based on the initial listens and the daily increase.

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

For the first song:

• Initial listens = 700
• Daily increase = 52
• Total listens after \( x \) days = \( 700 + 52x \)

For the second song:

• Initial listens = 600
• Daily increase = 56
• Total listens after \( x \) days = \( 600 + 56x \)

We set the two expressions equal to each other to find \( x \):

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

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 by 4:

\[ x = 25 \]

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