Entomology is the scientific study of insects. Patty, Ronny and Sammy collected some insects for their science project. At the end of the first week of collecting, Patty and Ronny together had 89 insects, Ronny and Sammy together had 80 insects, and Patty and Sammy together had85 insects. How many insects did each person have alone.

Question

Entomology is the scientific study of insects. Patty, Ronny and Sammy collected some insects for their science project.  At the end of the first week of collecting, Patty and Ronny together had 89 insects, Ronny and Sammy together had 80 insects, and Patty and Sammy together had85 insects.  How many insects did each person have alone.

I get the main idea, but i just don't know how to write it out. 
Thanks!!

Damon · Answer

P + R = 89
R + S = 80
P + S = 85

Now let's subtract equation 3 from equation 2
R - P = -5
now add that ot equation 1
P + R = 89
R - P = -5
------------
2 R = 84
so
R = 42
Now I will leave it to you to work your way back up and find P and S

Elizabeth · Answer

in the first step, what happened to the S? I understand how you got -5, but I don't understand what happened to S. i understand everything else, just that. would S = -5?