Question

OLD PROBLEM:Somebody asked a teacher: "How many students do you have? I would like to sendmy son to your school.” The teacher answered: “If as many students as I havenow join my school, and half as many as I have join it, and quarter as many, and yourboy comes to study with me as well; then I will have exactly 100 students.” Howmany students does the teacher have?

Answer 1

According to the given statement, let's imagine that the teacher has x students.

He says that if as many students as he has now join his school, it means you add x.

Then a half as many he has, which means you add 1/2x.

Then a quarter as many he has, you add 1/4x.

Finally, if the boy also joins the school, it means you add 1 and obtain a total of 100 students.

Write this in an equation and solve for x:

`\begin{gathered} x+x+(1)/(2)x+(1)/(4)x+1=100 \\ (11)/(4)x+1=100 \\ (11)/(4)x=99 \\ (1)/(4)x=(99)/(11) \\ x=9\cdot4 \\ x=36 \end{gathered}`

The teacher has 36 students.