Counting Siblings Word Problem: Linear Algebra Systems

Question: Alexandra and Brandon are brother and sister. We know that Alexandra has just as many brothers as sisters, and that Brandon has twice as many sisters as brothers. How many children are there in this family?

I am having trouble doing this problem. I've found a similar problem and solution but am having trouble with 2 aspects:

1) Why should bob have 2(sisters) = brothers? Doesn't this mean he has twice as many brothers as sisters, which will be the opposite as the question?

2) I don't understand how the author found the exact number of sisters and brothers. Did he/she just plug in random numbers until it worked?

3) Is there a way to do this with matrices. Isn't that the point of Linear Algebra.

Thank you so much!

let there be $g$ girls and $b$ boys in the family

Alexandra is a girl who has $g-1$ sisters and $b$ brothers

so $g-1=b$

Brandon is a boy who has $g$ sisters and $b-1$ brothers

so $2(b-1)=g$

can you take it from here ?

Seven.

If Alexandra has equal number of brother and sisters and Brandon has twice as many sisters as brothers, then brandon needs to have at least one brother.

So that way if brandon has one brother, there need to be two sisters for the second condition including Alexandra. But if brandon has a brother, Alexandra has two brothers and due to the 1st condition, she should have two sisters which increases the total number of girls to 3. Hence this is wrong.

So now if brandon has 2 brothers and 4 sisters including Alexandra, then for Alexandra there exist 3 brothers including Brandon and 3 sisters, which satisfies both conditions and is hence the correct answer.