Cayley Contest~~

Canadian Mathematics Competition
Thursday, February 25, 2010

"Obvious is the most dangerous word in mathematics." -- E.T. Bell


Ahhh! The math contest killed me. When I first began, it was like, I was so focused and so ready to answer all the questions, but as the end of the 60min period was approaching, it just made me all the more anxious. The 60 minutes passed by too quickly.. I remember looking back and forth at the clock. But although that was a bit of a distracting factor, it helped me to concentrate.
I answered as much as I could, and when Part B questions got too difficult for my brain to analyze, I skipped to Part C, but that wasn't any better. I spent a lot of time trying to figure out Part C questions, so I guess that's why I was so stressed!
But anyways, after it was all finished, I was just glad to get it over with, and a little worried about my answers when we went over them in class. But it was an interesting experience.. something that helped me realize how to deal with the anxiety and time pressure of exams, and helped me prepare for the provincial! =)

Soo this is one question from the Cayley contest that I picked to explain.
#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?

This was a bit tricky at first, and I think I had to do it twice because the first time I got an answer, I didn't have to think at all. Soo.. that was kind of weird, because it's a math contest. Just by looking at the ratio's 3:2 and 2:3, I quickly just added them together to get 5:5 and got answer (C) which is 1:1. That completely confused my brain, but I knew it couldn't be right.

Anyways, given the number of students for each school, I divided the ratio's to get how many girls and boys for each school.
(Pascal H.S. = 400 students; boys to girls = 3 : 2)
So I took the 400 total and divided it by 5 (3:2 ratio equals 5 parts when added together) and got 80. So that means there would be 80 students for every 1 part ratio. Since there are "3" boys, it would be 80x3 = 240. And same for the girls. 80x2 = 160. Just to be sure, 240 + 160 = 400, so I was sure that was correct.


And again using the same method for the second school.
Fermat C.I. = 600 students
boys to girls = 2 : 3
600/5 = 120 (120 students for every 1 part ratio)
120x2 = 240; 120x3 = 360
Double check: 240 + 360 = 600

That's the first part of the question, but by using the same method, I figured out the ratio for both schools put together.

Total boys from both schools: 240+240 = 480
Total girls: 160+360 = 520
So with 1000 students, the ratio of 480:520 when simplified (each divided by GCM:40) equals to 12:13.

Answers:
(A) 2 : 3
(B) 12 : 13
(C) 1 : 1
(D) 6 : 5
(E) 3: 2

My Answer: (B) 12 : 13