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)

Question

The songs will have the same number of listens after ___________ days.

Answer 1

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

For the first song:

• Initial listens: 700
• Daily increase: 52
• Number of listens after \( x \) days: \( 700 + 52x \)

For the second song:

• Initial listens: 600
• Daily increase: 56
• Number of listens after \( x \) days: \( 600 + 56x \)

We want to find the value of \( x \) when the two songs have the same number of listens, so we set the two equations equal to each other:

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

To solve for \( x \), we first simplify the equation:

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.