# How do I solve two equations in two unknowns?

In my free time, I've been challenging my mind with IQ problems. I found this question:

Jim has as many sisters as he has brothers, but his sister has twice as many brothers as she has sisters. How many boys and how many girls are there in the family?

I figured out that the answer is that there are 4 boys and 3 girls in the family. This is totally guessing though. I see many math problems like this with practice IQ questions and I'm trying to find a logical way to work these out on paper. With these problems, I'll figure out two math equations and then just insert numbers into them until I figure it out which doesn't seem like the right way to do it. For example, with this one I had (where $G$ is girl and $B$ is boy):

$$G = B - 1$$ (Because Jim would be one of the boys in the first condtion) and $$(G - 1)\times2 = B$$ (Because the sister would be one of the girls and then she had twice as many)

How do I do a comparison between two math problems? I'm obviously no math genius but I figured I'd reach out for help than try to search for an answer in my head that I don't believe I'll know :) Thanks so much for your help!

Let $B$ be the number of boys, and $G$ the number of girls.

First statement says that $B-1=G$, or $B=G+1$

Second one says that $G-1=B/2$, or $B=2G-2$

$G+1=2G-2$ implies that $G=3$, and of course $B=4$.

EDIT: changed variables names to fit with question.

• Ah of course, you compare the same variable against itself. It's obviously been a while since algebra for me :/ I'll accept your answer when they let me. Thanks! Oct 14, 2014 at 9:52
• You might have used the $B$ and $G$ variables the OP used in the question, rather than $A$ and $B$. Oct 14, 2014 at 10:04
• @HenningMakholm You are right, I will edit the answer. Oct 14, 2014 at 10:08
• G for boys and B for girls? o.O Oct 14, 2014 at 10:11
• Corrected - again! Oct 14, 2014 at 11:00