A family has several children. Each boy has as many sisters as brothers, but…
2023
A family has several children. Each boy has as many sisters as brothers, but each girl has twice as many brothers as sisters. How many brothers and sisters are there?
Answer: B. 4 boys and 3 girls — Let b = number of boys, g = number of girls. For any boy: sisters = g, brothers = b − 1. The condition says sisters = brothers, so g = b − 1. For any girl:…
- A.
5 boys and 4 girls
- B.
4 boys and 3 girls
- C.
3 boys and 4 girls
- D.
4 boys and 5 girls
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Correct answer: B
Let b = number of boys, g = number of girls.
For any boy: sisters = g, brothers = b − 1. The condition says sisters = brothers, so g = b − 1.
For any girl: brothers = b, sisters = g − 1. The condition says brothers = 2 × sisters, so b = 2(g − 1).
Substitute b = g + 1 (from the first equation) into the second: g + 1 = 2(g − 1) ⇒ g + 1 = 2g − 2 ⇒ g = 3.
Then b = g + 1 = 4, so there are 4 boys and 3 girls.
Check: For a boy, sisters = 3 and brothers = 3 (equal). For a girl, brothers = 4 and sisters = 2, and 4 = 2 × 2. Answer: 4 boys and 3 girls.