Birthdays

In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the class? (Note: All students in the class had a birthday on the day of the class. )

Result

n =  26

Solution:

n(n1)=650  n (n1)=650 n2n650=0  a=1;b=1;c=650 D=b24ac=1241(650)=2601 D>0  n1,2=b±D2a=1±26012 n1,2=1±512 n1,2=0.5±25.5 n1=26 n2=25   Factored form of the equation:  (n26)(n+25)=0  n=n1=26n*(n-1)=650 \ \\ \ \\ n \cdot \ (n-1)=650 \ \\ n^2 -n -650=0 \ \\ \ \\ a=1; b=-1; c=-650 \ \\ D=b^2 - 4ac=1^2 - 4\cdot 1 \cdot (-650)=2601 \ \\ D>0 \ \\ \ \\ n_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 1 \pm \sqrt{ 2601 } }{ 2 } \ \\ n_{1,2}=\dfrac{ 1 \pm 51 }{ 2 } \ \\ n_{1,2}=0.5 \pm 25.5 \ \\ n_{1}=26 \ \\ n_{2}=-25 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -26) (n +25)=0 \ \\ \ \\ n=n_{1}=26

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