Math
posted by Angie .
In a class of 550 students, students may take all, none, or a combination of courses as follows.?
Draw a Venn diagram to find how many students are not in any of these courses.
Mathematics280
Science200
Technology230
Mathematics and Technology110
Science and Technology100
Mathematics and Science80
Mathematics, Science, and Technology 20
I don't what numbers will go in each section of the Venn diagram and how you get the numbers..

start by drawing 3 intersecting circles, with an overlap of all 3 circles, label them M, S, and T for the 3 subjects.
Now fill in the values from the inside out.
20 take M, T, and S, so put that in the overlap of all 3
It says 110 take M and T, but we have already placed 20 of those 110, that leaves 90 to go into the region covered by M and S but NOT by T.
Repeat this process for the other two "doubles"
You should have 90 for M and T but not S,
and 80 for S and T but not M.
Now look at M only, it said that 280 take M, but we already have 170 in the M circle. That leaves 110 in the M circle which does not overlap anything else. Fill in the rest of the S and T circles the same way.
Now adding all those entries up should give you 440.
But there 550 students in the class, which means 110 would not be in any of the circles, thus not taking any of those 3 subjects. 
thank you!

But in this part, "It says 110 take M and T, but we have already placed 20 of those 110, that leaves 90 to go into the region covered by M and S but NOT by T." why can't you put it in M and T, when that was what 110 is for?

The answer is not 440 it is 430 if you add all those numbers together 110+90+20+60 by M this will give you 280. 30+90+20+90 by T will add upto 230 90+30+60+20= 200 and 30,90,60,20,30,90,110 Add upto 430 so what do you think did I made a mistake or did he/she?