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 as your variable. (1 point)

Question

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 as your variable. (1 point)

Answer 1

Let d be the number of days it would take for the two songs to have the same number of listens.

The total number of listens for the first song after d days is given by:
1000 + 38d

The total number of listens for the second song after d days is given by:
900 + 40d

Setting these two expressions equal to each other:
1000 + 38d = 900 + 40d

Now we solve for d:
38d - 40d = 900 - 1000
-2d = -100
d = 50

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