SOLUTION: A happy family had boys and girls. All the boys had equal number of brothers as they had sisters. All the girls had twice as many brothers as they had sisters... How many children

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Question 1087403: A happy family had boys and girls. All the boys had equal number of brothers as they had sisters. All the girls had twice as many brothers as they had sisters... How many children were there in all?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let the number of boys be b.
Let the number of girls be g.
Each boy has as many brothers as sisters, then
b-1+=+g......eq.1

but each girl has half as many sisters as brothers, so
g-1=+%281%2F2%29b
g=+%281%2F2%29b%2B1......eq.2

Solve the the system of equations by substituting for g:
b-1+=+%281%2F2%29b%2B1
b-2+=+%281%2F2%29b
%281%2F2%29b+=+2
b+=+4-> the number of boys

solve for g:
g=b-1
g+=+4-1
g+=+3-> the number of girls
the number of children in all 7