Mathcounts Marathon

Arghh!

Okay, Precalc coming up. Heh heh....

A man wants to build a rectangular enclosure for his herd. He only has $900 to spend on the fence and wants the largest size for his money. He plans to build the pen along the river on his property, so he does not have to put a fence on that side. The side of the fence parallel to the fence will cost $5 per foot to build, whereas the sides perpendicular to the river will cost $3 per foot. What dimensions should he choose?

EDIT: There's a reason why it's called MATHCOUNTS Marathon.

[Sillysidley]

Mathcounts only
Well, I guess we could do some easy algebra, geometry, and counting.
So only post easy-moderate problems of those type

Skipping the so-called precalc question:
If a square in a semicircle of radius r has area 8,find the area of a square in a circle of radius r.

Would've helped this year at state

Eh, I don't want to solve it now (it's very late in my time zone), so I'll just give the technique, and post the answer later. Divide square into two rectangles, use area of square, diagonals of rectangles (which are the radii of the semicircle) to find relationships between numbers, apply to full circle using the fact that full circle square's diagonal is diameter, done. Easy.


I wanna start an Olympiad or AIME topic!

[Sillysidley]

Yeah, we can so start an AIME topic. Or how about we start an AMC 10 or 12 topic right now, and later, when we're all sure we'll make AIME (around november or december) we make an AIME topic?

Okay. Next problem?

[Sillysidley]

Give an answer to my problem first

Oh come on. If I known how to, do I really have to actually do it?! (aka I'm lazy)

[Sillysidley]

Yup

Posted on AoPS to save myself the trouble.

[Sillysidley]

You did?