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!
Similar solutions: http://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.260308.html
Best Answer
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 ?