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.y

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 x as your variable.y

Answer 1

Let y be the number of days it would take for the two songs to have the same number of listens. The number of listens for the first song after y days is (1,000 + 38y), and the number of listens for the second song after y days is (900 + 40y).

Setting these two expressions equal to each other gives:

1,000 + 38y = 900 + 40y

Rearranging:

100 = 2y

Dividing by 2 on both sides gives:

50 = y

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