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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 number of listens. Use x
as your variable.(1 point)

1 answer

To find the equation that represents the number of days it would take for the two songs to have the same number of listens, we can set up the following equations based on the information provided:

  1. For the first song:

    • Initial listens: 1,000
    • Daily increase: 38 listens
    • After \(x\) days, the total listens will be: \[ 1000 + 38x \]

  2. For the second song:

    • Initial listens: 900
    • Daily increase: 40 listens
    • After \(x\) days, the total listens will be: \[ 900 + 40x \]

Next, we set the two expressions equal to each other to find out when the total listens will be the same: \[ 1000 + 38x = 900 + 40x \]

This is the equation that shows the number of days \(x\) it would take for the two songs to have the same number of listens.