It may be useful to use the Double Matrix Method to help us arrange our information. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.

Here, we have a population of theater patrons, and the two characteristics are:
- late or not late
- seated immediately or not seated immediately

So, we get the following:


Since this question concerns percents (instead of actual values), let's assign a "nice" value to the total number of theater patrons in this population. Let's say there are 100 theater patrons.



5 percent of the theater patrons are late and are seated immediately
The top left box is for theater patrons who are late and are seated immediately. So, 5% of the entire population will be in this box.



30 percent of the patrons who are late are not seated immediately
The patrons referred to here are those who go in the top right box. Unfortunately, we don't know the total number of patrons who are late, so we can't find 30% of that value.
So, let's let x = the total number of patrons who are late.



Now we can deal with this: 30 percent of the patrons who are late are not seated immediately


At this point, we know that the two top boxes must have a sum of x.
So, we can write: 5 + 0.3x = x (now solve)
Rearrange: 5 = 0.7x
Divide: 5/0.7 = x
Or 50/7 = x
Approximate: 7.something = x

Since x represents the total number of patrons who are late, we know that about 7 out of 100 patrons are late.
In other words, about 7% of the patrons are late.

Answer: B

To learn more about the Double Matrix Method, watch this video: