Question 1111858: Amongst the children in a family, each boy has as many sisters as brothers, but each girl has only half as many sisters as brothers. Find the number of children in the family.
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
Answer. 4 boys and 3 girls. 7 children, in all.
Solution
Let b be the number of boys and g be the number of girls.
Then
b - 1 = g (1) ("each boy has as many sisters as brothers")
2*(g-1) = b (2) ("each girl has only half as many sisters as brothers")
First equation says "each boy has b-1 brothers, and this number is equal to the number of sisters".
Second equation says "each girl has g-1 sisters, and .. . and so on . . . ")
From (1), substitute "b" into (2) and get the answer.
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Solved.
Thanks for this entertainment problem posted.
It was a pleasure to solve it.
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Comment from student: I didn't understand the wording, but I'm glad that you enjoyed it. Thanks for answering.
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My responce: I Emailed this problem today late in the evening to two my grandsons.
One of them is 12-th grade; the other is 11-th grade.
To my great satisfaction, both returned me their correct solutions less than in half an hour.
I was very happy !
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