A family has several children each boy in the family has many sisters as brothers and each girl has twice as many brothers as sisters how many brothers and sist

Question

Simplication question

 

Answer 1

Let b = number of boys

      g = number of girls

 

Note that each boy has (b-1) brothers and g sisters.

             Each girl has b brothers and (g-1) sisters.

 

"each boy in the family has as many sisters as brothers"

       means                                      g       =      (b-1)           [eq1]

 

"each girl has twice as many brothers as sisters"          means

                                             b   =   2*(g-1)                    [eq2]

 

Use the value for g in [eq1] to substitute into [eq2]:

        b = 2 * ( (b-1) - 1)

        b = 2(b-2)

        b = 2b - 4

        4 = b

    There are 4 boys.

 

Now, use either [eq1] or  [eq2] to solve for g:

     g = b-1

     g = 4-1

     g = 3

   There are 3 girls.

 

Check:

    Does ""each boy in the family has as many sisters as brothers" ?
                3 brothers and 3 sisters
                3 = 3 ?yes

   Does "each girl has twice as many brothers as sisters"    ?

                 4 brothers and 2 sisters

                     4 = 2*2   ?   yes