Question

A family has several children. Each boy in the family has as many sisters as brothers but each girl has twice as many brothers as sisters. How many brothers and sisters are there?

• A. 3 Brothers, 4 Sisters
• B. 4 Brothers, 4 Sisters
• C. 4 Brothers, 3 Sisters
• D. Cannot say

Answer 1

The Correct Option is C

To solve the problem, let's define the variables:

• Let b be the number of boys (brothers).
• Let g be the number of girls (sisters).

According to the problem:

1. Each boy has as many sisters as brothers. Since each boy has (b - 1) brothers, they also have g sisters, therefore:
   b - 1 = g
2. Each girl has twice as many brothers as sisters. Since each girl has (g - 1) sisters, they have b brothers, hence:
   b = 2(g - 1)

We now have two equations:

(1) b - 1 = g
(2) b = 2(g - 1)

Let's solve these equations.

1. Substitute g from equation (1) into equation (2):
   b = 2((b - 1) - 1)
2. Open up the equation:
   b = 2(b - 2)
3. Simplify the equation:
   b = 2b - 4
4. Rearrange to solve for b:
   b - 2b = -4
   -b = -4
   b = 4
5. Substitute the value of b back into equation (1) to find g:
   4 - 1 = g
   g = 3

Thus, the family has 4 brothers and 3 sisters, matching the option: 4 Brothers, 3 Sisters.