Question

at an annual function of a school,each student gives gift to every other student. If the number of gifts is 1980,find the number of students

Answer 1

let the number of students be X

if each student gives gifts to every other student , then each student has to carry (X-1) gifts .

so , total number of gifts is given by,
X * (X-1) = 1980
X^2 - X = 1980
X^2 - X - 1980 = 0
X^2 - 45X + 44X -1980 = 0
X(X - 45) + 44 (X - 45) = 0
X = 45 or X = -44

as the number of students is always positive , X= 45

so there are 45 students.