SOLUTION: Every student in a 2nd grade class sends a valentine to each of the other students in the class, for a total of 306 valentines. How many students are in the class?

Question 248704: Every student in a 2nd grade class sends a valentine to each of the other students in the class, for a total of 306 valentines. How many students are in the class?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
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

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