1. ## Set Problems

Ok, I've done these types of problems before, but now I'm not given an intersections. Here is the problem:

At a school fair 34 students are given awards for projects. 14 awards were given for biology, 13 in chemistry and 21 in physics. If 3 students are given awards in all three subject areas how many awards are received for one subject area and and 2 subject areas?

So here is what I've started on...

I just don't know where to go without the intersections I guess? Help on this would be much appreciated!

Ok, I've done these types of problems before, but now I'm not given an intersections. Here is the problem:

At a school fair 34 students are given awards for projects. 14 awards were given for biology, 13 in chemistry and 21 in physics. If 3 students are given awards in all three subject areas how many awards are received for one subject area and and 2 subject areas?

So here is what I've started on...

I just don't know where to go without the intersections I guess? Help on this would be much appreciated!
There were 34 students awarded prizes. 3 of these recieved a prize in each subject, leaving 31 students to split the rest.

Personally, I would stick this all into a formula (well, actually, two formulas),

$\displaystyle n$ students got 1 prize,

$\displaystyle m$ students got 2 prizes, so

Note that $\displaystyle n+m = 34-3=31$, and that $\displaystyle n+2m = (13-3) + (21-3) + (14-3) = 39$. Solve.

Do you understand where I got these two equations from? The first is just counting the number of students, the second the number of awards.