help.. matrices question!

[soNasty]

hey guys, i came across this question in one of my exams (kilbaha 2011) and im unsure as to why the answer is E rather than B... the two equations i used were
20x+8y=40900 and x+y=3200
where x is the number of adults and y is the number of children attending
it says in the answers that they converted the 20x+8y=40900 into 5x+2y=10225.. but why not leave it as it is?
thank you

[sjayne]

20x +8y=40900 can be simplified to 5x+2y=10225
therefore

|1  1| x|x|=|3200  |
|5  2|   |y|  |10225|
A       x  X = B
and A^-1 x B=X

Next you find the inverse of A and multiply it by B
1/2x1-5x1 |2  -1|x|3200  |
                 |-5  2|  |10225|

[soNasty]

20x +8y=40900 can be simplified to 5x+2y=10225
therefore

|1  1| x|x|=|3200  |
|5  2|   |y|  |10225|
A       x  X = B
and A^-1 x B=X

Next you find the inverse of A and multiply it by B
1/2x1-5x1 |2  -1|x|3200  |
                 |-5  2|  |10225|

yes but why would you even need to simplify it?
and why isnt B right!

[plato]

I agree with you.
There is no point in simplifying an equation if you are going to use matrices anyway. All this does is to introduce an unnecessary step where an error could be made.

I seems Kilbaha just wants you to jump another hurdle to make it seem more difficult.

[sjayne]

it is a bit odd :/

[soNasty]

very odd and pointless, stupid kilbaha.

[Patches]

That's stupid, really can't see that coming up in a VCAA exam.