SOLUTION: A boy says "I have the same number of sisters as I have brothers". His sister says "I have twice as many brothers as I have sisters". How many sons and how many daughters do th

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Question 515123: A boy says "I have the same number of sisters as I have brothers".
His sister says "I have twice as many brothers as I have sisters".
How many sons and how many daughters do their parents have?
Found 2 solutions by htmentor, Edwin McCravy:
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
In the question how many brothers and sister you have the brother has answered "i have as many sisters as brothers" in the other hand the sister answers "i have twice more brothers than sisters". How many brothers and sisters are they?
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Let B = the total number of brothers
Let S = the total number of sisters
When the brother is asked, he doesn't count himself so we can write:
B - 1 = S [same number of brothers and sisters]
When the sister is asked, likewise she doesn't count herself, so we have:
2(S - 1) = B [twice as many brothers as sisters]
Solve for B in the 1st equation and substitute into the 2nd:
2(S - 1) = S + 1
This gives S = 3
So there are 3 sisters and 4 brothers

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A boy says "I have the same number of sisters as I have brothers".
His sister says "I have twice as many brothers as I have sisters".
How many sons and how many daughters do their parents have?
Let S = the number of sons
Let D = the number of daughters

The number of sisters the boy has is the same as the number of daughters.

The number of brothers the boy has is 1 less than the number of sons,
because he is not his own brother.

The number of brothers the girl has is the same as the number of sons.

The number of sisters the girl has is 1 less than the number of daughters,
because she is not her own sister.

So,

NUMBER OF HIS SISTERS = NUMBER OF DAUGHTERS
NUMBER OF HIS BROTHERS = NUMBER OF SONS - 1 
NUMBER OF HER BROTHERS = NUMBER OF SONS
NUMBER OF HER SISTERS = NUMBER OF DAUGHTERS - 1

The first equation comes from:

NUMBER OF HIS SISTERS = NUMBER OF HIS BROTHERS 
  NUMBER OF DAUGHTERS = NUMBER OF SONS - 1
                    D = S - 1

The second equation comes from:

NUMBER OF HER BROTHERS = 2*(NUMBER OF HER SISTERS) 
        NUMBER OF SONS = 2*(NUMBER OF DAUGHTERS - 1)
                     S = 2(D - 1)

       Solve the system of equations:

                     D = S - 1
                     S = 2(D - 1)

Solve that and get D = 3, S = 4.

So their parents have 3 daughters and 4 sons.

Edwin