Question 248704
let x = number of valentine lovers in the class
They each send valentines to x-1 students.
And what about the poor unloved teacher getting one.
We always gave valentines to the teacher too.
x*(x-1)=306
x^2-x=306
x^2-x-306=0
we want factors of 306 which have  a difference of 1
try 17 and 18
(x-18)(x+17)=0
x=18 
x=-17 although the teachers might like it we can't have a negative number of students.
so 18 students send 17 valentines each