Step-by-Step Algebraic Solution

This problem can be solved by setting up a system of two linear equations with two variables based on the two statements provided.

1. Define the Variables

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

2. Formulate the Equations

We can translate each statement into a mathematical equation:

1. "Each boy ... has as many sisters as brothers."
   • From a boy's perspective, the number of his brothers is the total number of boys minus himself (b - 1).
   • The number of his sisters is the total number of girls (g).
   • This gives us our first equation: g = b - 1
2. "...each girl has twice as many brothers as sisters."
   • From a girl's perspective, the number of her sisters is the total number of girls minus herself (g - 1).
   • The number of her brothers is the total number of boys (b).
   • This gives us our second equation: b = 2 × (g - 1)

3. Solve the System of Equations

We can now solve these two equations. Let's substitute the first equation (g = b - 1) into the second one:

b = 2 × ( (b - 1) - 1 )

b = 2 × (b - 2)

b = 2b - 4

4 = 2b - b

b = 4

Now, we find the number of girls (g) using the first equation:

g = b - 1 = 4 - 1

g = 3

Conclusion

There are 4 brothers and 3 sisters in the family.