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A boy has as many sisters as brothers, but each sister has only half as many sisters as brothers.
How many brothers and sisters are there in the family?
Tags:
4 boys and 3 girls
correct
Let B = number of boys and G = number of girls
For each boy, the number of brothers is B - 1 (number of boys excluding himself) and the number of sisters is G. It’s given that B - 1 = G (1)
For each girl, the number of sisters is G - 1 (number of girls excluding herself) and the number of brothers is B. It’s given that G - 1 = 0.5 · B (2)
So, by solving the simultaneous equations (1) and (2), we can get the number of children.
Rearranging (1), B = G + 1 (3)
Substituting (3) into (2), G - 1 = 0.5 · (G + 1) (4)
Solving (4) for G as follows:
2G - 2 = G + 1
G = 3
Substituting G = 3 into (3), we get B = 3 + 1 = 4
Therefore, 3 girls and 4 boys.
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