<p>I knew how to do this before, I just forgot.. kinda sad..</p>
<p>here's the question:
of the 850 stores in Noel Bentley County, 250 have alarm systems and 450 have guard dogs. If 350 stores have neither alarm systems no guard dogs, then how many stores have both alarm systems and guard dogs?</p>
<p>200 have both alarm systems and guard dogs, because if we have 850 stores, and 350 have neither, then that means that 500 stores have at least one thing. Now we know that 250 have alarms and 450 have dogs, so we want to know how many extra stores we have here. 250 + 450 = 700. We were only supposed to have 500 left, so that means that 200, (because 700 - 500), have both. Then 50 have alarms, and 250 have guard dogs. Check your work by adding it all up in the end. 350 stores with nothing + 200 with both + 50 with alarms + 250 with dogs = 850 stores in all</p>
<p>Thank you so much for the reply. 
its clear to me now.</p>
<p>Another way to put it is, there are 500 stores with at least one type of security. By the Inclusion-Exclusion principle,</p>
<p>250 + 450 - x = 500, where x is the number of stores with both types of security. Therefore x = 200.</p>