Birthdays

In a classroom, students give candy to their classmates on their birthdays. The birthday student gives one candy to each classmate but does not receive one themselves. A total of 650 candies were given out over the course of the year. How many students are in the class? (Assume every student had their birthday on a school day.)

Final Answer:

n =  26

Step-by-step explanation:

$$\begin{gathered} n\cdot (n-1)=650 \\ n\cdot (n-1)=650 \\ {n}^2-n-650=0 \\ a=1;b=-1;c=-650 \\ D=b^2-4ac=1^2-4\cdot 1\cdot (-650)=2601 \\ D>0 \\ {n}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{1\pm \sqrt{2601}}{2} \\ {n}_{1,2}=\frac{1\pm 51}{2} \\ {n}_{1,2}=0.5\pm 25.5 \\ {n}_1=26 \\ {n}_2=-25 \\ n=n_1=26 \end{gathered}$$

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