Question

One professor passes by a group of students and he said hello one hundred students and the students respond hello professor, however we are not one hundred. But if you add our number plus our number, plus half our number, plus quarter our number, plus you we are hundred students.what is the number of the students?

Answer 1

let x be the real number of the students, we have the following equation

$\begin{gathered} x+x+\frac{x}{2}+\frac{x}{4}+1=100 \\ 2x+\frac{x}{2}+\frac{x}{4}=100-1=99 \\ \frac{8x}{4}+\frac{2x}{4}+\frac{x}{4}=99 \\ \frac{11x}{4}=99 \\ x=99\cdot\frac{4}{11}=9\cdot4=36 \end{gathered}$

so the number of students is 36