Cayley math contest

MATH CONTEST. ahhh. I did not expect this when I went into the cafeteria to take it. IT WAS SO HARD. well part A was really easy. I did it first so because i knew i would finish those fastest and then I would have more time to finish the harder ones knowing i had already finished some. Section B was pretty tough, it took time and thought. Every time I finished a question in section B it felt like a victory and i felt a little bit smarter.Then there was section c. IT WAS SO HARD. I didn't get any of them. I was disappointed that i didn't even do one of section c. When we were going over the question in class I felt kind of stupid. Mr Cheng made it look so easy. I found myself thinking HOW DID I NOT GET THAT many times. My favorite question of the contest was #10. There are 400 students at Pascal H.S., where the ratio of boys to girls is 3 : 2. There are 600 students at Fermat C.I., where the ratio of boys to girls is 2 : 3. When considering all the students from both schools, what is the ratio of boys to girls?

I liked this question because when i first looked at it I was confused. But after reading it a couple of times I saw that it wasn't so hard. This is what i did.
Pascal HS:
boys to girls: 3:2
# of students: 400
Fermat CI
boys to girls is 2:3
# of students: 600

What I did was try to find out how many student were for every "1" part of the ratio.
So for Pascal HS there are 400 students and together there are '5' parts of the ratio. So 400/5 = 80
That means each one part is equal to 80 students. Which means there are 240 boys and 160 girls. all equaling 400.
For Fermat CI there is 600 students. So 600/5= 120. Which means there are 240 boys and 360 girls.
Together from both school the ratio of boys to girls is 480: 520 or 12: 13