SOLUTION: the children in a family comprise both boys and girls. Each boy has as many brother as sisters, but each girl has half as many sisters as brothers. how many boys and how many girls

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Question 433042: the children in a family comprise both boys and girls. Each boy has as many brother as sisters, but each girl has half as many sisters as brothers. how many boys and how many girls are in the family
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the children in a family comprise both boys and girls. Each boy has as many brother as sisters, but each girl has half as many sisters as brothers. how many boys and how many girls are in the family.
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Let # of boys be "b".
Let # of girls be "g".
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Each boy has as many brothers as sisters
b-1 = g
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but each girl has half as many sisters as brothers.
g-1= (1/2)b
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Solve the the system of equations by substituting for "g":
b-1-1 = (1/2)b
b-2 = (1/2)b
(1/2)b = 2
b = 4 (# of boys)
----
solve for "g":
b-1 = g
g = 4-1 = 3 (# of girls)
============================
Cheers,
Stan H.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The children in a family comprise both boys and girls. Each boy has as many
brother as sisters, but each girl has half as many sisters as brothers. how
many boys and how many girls are in the family?
Let b = the number of boys.
Let g = the number of girls.

Each boy has one less brother than the number of boys, since he is not his 
own brother, so

b-1 = the number of brothers each boy has.

However

b = the number of brothers each girl has.

Each girl has one less sister than the number of girls, since she is not 
her own sister, so

g-1 = the number of sisters each girl has.

However

g = the number of sisters each boy has.

>>...Each boy has as many brother as sisters...<<

            b-1 = g


>>...each girl has half as many sisters as brothers...<<

           g-1 = ½b

Clear that equation of fractions by multiplying through by 2

          2g-2 = b

Substitute b-1 for g

      2(b-1)-2 = b
        2b-2-2 = b  
          2b-4 = b
            2b = b+4
             b = 4

Substitute 4 for b in

            b-1 = g
            4-1 = g
              3 = g

So there are 4 boys and 3 girls in the family.  Each boy has 
3 brothers and 3 sisters.  Each girl has 2 sisters and 
4 brothers.

Edwin