The Oddville Academy offers three languages: Oriya, Dakhini, and Dutch (how odd!). Each student takes an odd number of languages – that is, every student takes either one language or three languages. Let $x$ be the number of students taking Oriya, $y$ be the number of students taking Dakhini, $z$ be the number of students taking Dutch, and $t$ be the number of students taking all three languages. Find an expression in terms of $x, y, z,$ and $t$ for the total number of students at the Oddville Academy.
Cheating in AoPS??
I won't solve it, but I'll give you a helpful start.
Clearly, if we add up everything, then we would overcount, which we do not want. We want to count things once and only once. (Sound Familiar)
Now, make an expression where you add up everyone. The subtract that by two times the people who did all languages. (I technically gave you the answer.)
Hope that helps!!!