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.

Guest Jun 2, 2017

#2**+2 **

You are very observant about those first letters ZZZ... but your logic is just a little off :))

There are t students taking all three and the rest take only 1 language so

The number taking **only** Oriya is x-t

The number taking **only** Dakhini is y-t

The number taking **only** Dutch is z-t

So the number of students altogether is

x-t + y-t + z-t + t = **x+y+z-2t**

Melody
Jun 2, 2017

#1**+2 **

x+y+z+t=number of students at Oddville Academy

(Also I noticed that the languages' first letters spell "odd")

ZZZZZZ
Jun 2, 2017

#2**+2 **

Best Answer

You are very observant about those first letters ZZZ... but your logic is just a little off :))

There are t students taking all three and the rest take only 1 language so

The number taking **only** Oriya is x-t

The number taking **only** Dakhini is y-t

The number taking **only** Dutch is z-t

So the number of students altogether is

x-t + y-t + z-t + t = **x+y+z-2t**

Melody
Jun 2, 2017