Mathematics
posted by Anonymous on .
Among 500 freshmen pursuing a business degree at a university, 313 are enrolled in an economics course, 205 are enrolled in a mathematics course, and 153 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in
(a) An economics and/or a mathematics course?
(b) Exactly one of these two courses?
(c) Neither an economics course nor a mathematics course?

So out of 500 students, we know what 671 of them are doing. I think there are many unregistered freshman taking classes at that college. ...
The numbers do not add up. 
I may have read this wrong, of course. After reading it again, I thought differently.
There are 153 students taking both economics and math. That means there are:
205  153 = 52
There are 52 students only taking math, but not economics.
313153 = 160
So 160 students are taking economics without math.
So out of 500, we have:
160 only taking economics.
52 only taking math.
153 taking both.
That is 365 out of 500 taking at least one of the classes. How many aren't taking math or economics?
Now, it's just a matter of percentages. 
Half of a third of x equals a fourth of y plus a fifth of y. If x = 27, what is the value of y?

4 and 5