Question

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 days.

Answer 1

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

The number of listens for the first song after \( x \) days can be expressed as: \[ 700 + 52x \]

The number of listens for the second song after \( x \) days can be expressed as: \[ 600 + 56x \]

To find out when the two songs will have the same number of listens, we set the two expressions equal to each other: \[ 700 + 52x = 600 + 56x \]

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

First, we can rearrange the equation: \[ 700 - 600 = 56x - 52x \] \[ 100 = 4x \]

Now, divide both sides by 4: \[ x = 25 \]

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