Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long. If Colby's video is 101 minutes long, how many skits are in his video?

From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).

So, we need to write the following equations:

First equation:

[tex]TotalDuration=Introduction+n*Skit[/tex]

Second equation:

[tex]Skit=6Minutes[/tex]

Where,

[tex]TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes[/tex]

So, replacing and substituting the second equation into the first equation we have:

[tex]101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16[/tex]

So, there are a total of 16 skits in the video.

Let's prove it substituting "n" into the first equation:

[tex]101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes[/tex]

Have a nice day!