If you’re taking the test tomorrow morning, you should ignore this and REST YOUR BRAIN. If you’re not taking it tomorrow, though, then this is just another regular weekend for you, and you should work your brain HARD.

The prize, as it has been every week for weeks and weeks, is access to the coveted PWN the SAT Math Guide Beta. If you wanna win, you have to comment in such a way that I can contact you. Preferably using Facebook, Twitter, or Gmail.

A warning: this one is pretty tough.

In a hand in his weekly poker game, Mike won money from both John and Sean. Mike’s percent gain on the hand was equal in magnitude to John’s percent loss. John bet twice as much as did Sean. Mike and John together held \$200 in chips before the hand began. If Sean bet \$20 in chips on the hand, what was Mike’s chip total after the hand was over?

Good luck!

UPDATE: Nobody got this yet, so I’m gonna leave it up for now unanswered. If you solve it, book access is yours.

SECOND UPDATE: OK, Eowyn got it. Nice. Solution below the cut.
There’s a lot going on here, and at first blush it may seem as though you have too many variables to work with. If you write down everything you know, though, and play around with it enough, you’ll see that you can actually get it down to just one variable in one equation!

$percent\:&space;change&space;=&space;\frac{change}{original\:&space;value}\times&space;100\%$
$\frac{Mike's\:gain}{Mike's\:original\:value}\times&space;100\%&space;=&space;\frac{John's\:loss}{John's\:original\:value}\times&space;100\%$

Of course, we can tidy this up a bit:

$\frac{Mike's\:gain}{Mike's\:original\:value}&space;=&space;\frac{John's\:loss}{John's\:original\:value}$

Now we need to start figuring out the numbers. We know that Sean bet 20, and that John bet twice as much as Sean. So John bet 40, which means John’s loss was 40. We also know that Mike’s gain was 60, since he won all the money that was bet in the hand (John’s 40 + Sean’s 20).

$\frac{60}{Mike's\:original\:value}&space;=&space;\frac{40}{John's\:original\:value}$

And we can be a bit clever here if we want to jam all the info into one equation and say that, since Mike’s and John’s chips added up to 200 before the hand, Mike’s prior chip total can be m, and John’s prior chip total can be 200 – m.

$\frac{60}{m}&space;=&space;\frac{40}{200-m}$

Solve that for m

$40m&space;=&space;60(200-m)$
$40m&space;=&space;12000-60m$
$100m&space;=&space;12000$
$m&space;=&space;120$

…and you’ll see that before the hand began, Mike had 120 dollars in chips. Since he won 60, he has 180 after the hand.