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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 !