15. The number of girls varied directly as the number of boys and inversely as the number of teachers. When there were 50 girls, there were 20 teachers and 10 boys. How many boys were there when there were 10 girls and 100 teachers?

Number of boys were

Step-by-step explanation:

According to Direct proportion:

When varies directly with then , {where is proportionality                            

                                                                                             constant}.

Let number of girl be ,

Number of boy be ,

And number of teacher be .

From the question,

Number of girls varies directly as the number of boys and inversely with number of teacher.

So, Using direct proportion we get an equation

                                           ........(a)

Case 1: ,   ,   and

Now,  substituting all the values in equation (a) we get,

               ⇒

Case 2: ,   ,

Finding the number of boys using   we get,

                ⇒

Therefore, Number of boys were