Question

At the beginning of the month, a video on a streaming service already had 2130 views, and was getting 80 new views each day. Meanwhile, a video on a different service already had 1800 views and was getting 90 new views each day. Write an equation to show the number of days it would take for the two videos to have the same number of views.

Answer 1

To find the number of days it will take for the two videos to have the same number of views, we can set up equations for the number of views for each video as a function of time in days.

Let \( d \) be the number of days.

1. For the first video:
- Initial views: 2130
- Daily views increase: 80
- Total views after \( d \) days: \( 2130 + 80d \)

2. For the second video:
- Initial views: 1800
- Daily views increase: 90
- Total views after \( d \) days: \( 1800 + 90d \)

To find out when the two videos will have the same number of views, we set the two equations equal to each other:

\[
2130 + 80d = 1800 + 90d
\]

Now, we can solve for \( d \).

First, we can subtract \( 80d \) from both sides:

\[
2130 = 1800 + 10d
\]

Next, subtract 1800 from both sides:

\[
2130 - 1800 = 10d
\]

This simplifies to:

\[
330 = 10d
\]

Finally, divide both sides by 10:

\[
d = 33
\]

Thus, it will take 33 days for the two videos to have the same number of views.