In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family ?
Question
In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family ?
Solution
Let's denote the number of daughters by D and the number of sons by S.
From the problem, we have two equations:
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Each daughter has the same number of brothers as she has sisters. This means that the number of brothers a daughter has (which is the number of sons in the family) is equal to the number of sisters she has (which is the number of daughters minus one, because a girl is not her own sister). So, we have the equation: S = D - 1.
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Each son has twice as many sisters as he has brothers. This means that the number of sisters a son has (which is the number of daughters in the family) is twice the number of brothers he has (which is the number of sons minus one, because a boy is not his own brother). So, we have the equation: D = 2*(S - 1).
Now, we can solve these two equations to find the values of D and S.
Substitute the first equation into the second equation, we get: S = 2*(S - 1) - 1. Simplifying this equation, we get: S = 2S - 2 - 1, or S = 3.
Substitute S = 3 into the first equation, we get: 3 = D - 1, or D = 4.
So, there are 3 sons and 4 daughters in the family.
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