Question

Each girl in the Limburg family has the same number of brothers and she has sisters. Each boy in the Lindbergh family has twice as many sisters as he has brothers. How many girls and boys are there in the Lindbergh family

Answer 1

Let \( g \) represent the number of girls and \( b \) represent the number of boys in the Lindbergh family.

From the problem, we know the following:

1. Each girl in the Limburg family has the same number of brothers and sisters:
- Since there are \( b \) boys and \( g \) girls, each girl has \( b \) brothers and \( g - 1 \) sisters (she does not count herself).
- We have the equation:
\[
b = g - 1
\]
This indicates that each girl has the same number of brothers (b) and sisters (g - 1).

2. Each boy in the Lindbergh family has twice as many sisters as he has brothers:
- Since each boy has \( g \) sisters and \( b - 1 \) brothers (he does not count himself), we can express this as:
\[
g = 2(b - 1)
\]

Now we have two equations:
1. \( b = g - 1 \)
2. \( g = 2(b - 1) \)

Substituting the first equation into the second:
\[
g = 2((g - 1) - 1)
\]
\[
g = 2(g - 2)
\]
\[
g = 2g - 4
\]
Now, we can rearrange the equation:
\[
g - 2g = -4
\]
\[
-g = -4
\]
\[
g = 4
\]

Now, plug \( g \) back into the first equation to find \( b \):
\[
b = g - 1 = 4 - 1 = 3
\]

Thus, the number of girls and boys in the Lindbergh family is:
\[
\text{Number of girls} = 4, \quad \text{Number of boys} = 3
\]

In conclusion, the Lindbergh family has **4 girls and 3 boys**.