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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.(2 points)
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1 answer

To find the number of days it would take for the two songs to have the same number of listens, we can set up equations for the total listens of each song over time.

Let:

  • Song A has an initial listen count of 1,000 and receives 38 new listens each day.
  • Song B has an initial listen count of 900 and receives 40 new listens each day.

We can express the number of listens for each song after \( x \) days as follows:

  • For Song A: \[ \text{Listens}_A = 1000 + 38x \]

  • For Song B: \[ \text{Listens}_B = 900 + 40x \]

To find the number of days \( x \) at which both songs have the same number of listens, we set the two expressions equal to each other:

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

Now, we can solve for \( x \):

  1. Subtract \( 38x \) from both sides: \[ 1000 = 900 + 2x \]

  2. Subtract 900 from both sides: \[ 100 = 2x \]

  3. Divide both sides by 2: \[ x = 50 \]

So the equation that represents the situation is:

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

And the solution shows that it will take \( x = 50 \) days for the two songs to have the same number of listens.