Question

A boy has as many sisters as brothers , and his sisters have half as many sisters as brothers. How many boys and girls are there in the family.

Answer 1

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, the answer is 3 girls and 4 boys