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.

Answer 1

Let's assume that after x number of days, both songs will have the same number of listens.
Thus, the equation representing the number of listens for the first song after x days is: 1000 + 38x.
Similarly, the equation representing the number of listens for the second song after x days is: 900 + 40x.

Setting these two equations equal to each other, we have:
1000 + 38x = 900 + 40x.

Simplifying the equation, we get:
38x - 40x = 900 - 1000,
-2x = -100.

Dividing both sides by -2, we find:
x = 50.

Therefore, it will take 50 days for the two songs to have the same number of listens.