Lesson How many boys and how many girls are there in a family ?

How many boys and how many girls are there in a family ?

Problem 1

Let "b"  be the number of boys.
Let "g"  be the number of girls.


Each boy has as many brothers as sisters

    b-1 = g         (1)


Each girl has half as many sisters as brothers

    g-1 = (1/2)b    (2)


Solve the the system of equations by substituting for "g":

    (b-1)-1 = (1/2)b

     b-2 = (1/2)b

     b - (1/2)b = 2

     b = 4              (the number of boys)


Now solve for "g":


    b-1 = g
    g = 4-1 = 3         (the number of girls)


ANSWER.  4 boys and 3 girls.

Problem 2

From the condition, the number of boys in the family is 6 more than sisters.


So, one equation is

    b + g = 10


The second equation is

    b - g = 6.


Add the equations and find  b = 8, g = 2.


Answer.  There are 8 boys and 2 girls in the family.

Problem 3

1.  It follows from the first two sentences that the child who says it, is a girl.



2.  So, the girl has two more sisters than brothers:


    g -1 = b + 2,    or   g = b + 3,


    where "g" is the number of girls and "b" is the number of boys in the family.


    Hence, each boy (each brother) has 4 more sisters than brothers.