at the beginning of the month a song on a streaming service already had 1,000 listens and was getting 38 new listens each day meanwhile, a different song already had 900 listens. and was getting 40 new listens each day. write an equation to show the number of days it would take for the two songs to have the same nunber of listens. use x as variable

Answer 1

Let's define the number of listens for each song in terms of the variable \( x \), which represents the number of days.

1. First Song:

   • Initial listens: 1,000
   • New listens per day: 38
   • Total listens after \( x \) days: \[ 1000 + 38x \]

2. Second Song:

   • Initial listens: 900
   • New listens per day: 40
   • Total listens after \( x \) days: \[ 900 + 40x \]

To determine when the two songs have the same number of listens, we set the equations equal to each other:

\[ 1000 + 38x = 900 + 40x \]

Now, you can solve this equation for \( x \).