# Thread: Set Problems

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!

2. Originally Posted by intervade
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),

$n$ students got 1 prize,

$m$ students got 2 prizes, so

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