Question

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

Answer 1

hey dear


here is your answer


_________________________________


given


each student gives a gift to student

number of gift = 1980



it means the way that student given gift in the form of x ( x - 1 )



x ( x - 1 ) = 1980


x^2 - x =1980


x^2 - x = 1980


x^2 - x - 1980 = 0


we use splitting the middle terms


we do prime factor of 1980 Is

2*2 *3*3 *5 *11


so we adjust these factor in this way that when we multiply it come 1980 and by adding or subtracting it come middle value which means - x


so,


x^2 - x - 1980 = 0


x^2 - 45x + 44x - 1980 = 0.


x ( x - 45 ) + 44 ( x - 45 )


( x + 44 ) , ( x - 45 )


as we know that x can't be negative



hence x = 45


number of students are 45


__________________________________


hope it helps

thank you