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Taylor is comparing the success of these two songs. She wants to write an equation that would show how many days it would take for the two songs to have the exact same number of streams. She used x for the days that have passed. Which equation is correct?

To refresh your memory:
Song #1) You Belong With Me had 580 million streams on Spotify. It was gaining 0.4 million new listens each day.
Song #2) Karma, only had 565 million streams but was gaining 1 million streams per day.

3 answers

Let \( x \) represent the number of days that have passed.

For Song #1 ("You Belong With Me"):

  • Initial streams: 580 million
  • Daily gain: 0.4 million streams

The number of streams after \( x \) days would be: \[ 580 + 0.4x \]

For Song #2 ("Karma"):

  • Initial streams: 565 million
  • Daily gain: 1 million streams

The number of streams after \( x \) days would be: \[ 565 + 1x \]

To find the number of days it takes for the two songs to have the same number of streams, we can set the two expressions equal to each other:

\[ 580 + 0.4x = 565 + 1x \]

This is the correct equation to determine when the number of streams for both songs will be the same.

Using your answer for Question 3, indicate how many solutions the equation in Question 3 would have. Then indicate how many days would have to pass for each song to have the same exact number of streams. In other words, solve the equation in Question 3.
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