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## June 22, 2005

### Geek attack: math whiz blogg'd

I can't believe how smart I feel.

Tomorrow is the last day of my math class, and we have an exam (of course). The teacher gave us three word problems to take home to do so they wouldn't eat all the time we'd need for the exam.

So the first two aren't awful, but they're more difficult...

Then there's the third problem. What a monster! A word problem that involved setting up the equations (which I'm horrible at), making a table, using derivatives, linear combinations, negative and positive numbers in ugly combinations, and all to find out how many little ceramic wreaths, trees, and sleds this Christmas shop can make in the amount of time they have...

I screwed it up the first three times I did it. How did I know that? Well, the answers I got were the ugliest fractions-turned-decimals I've ever seen in my life. Or they were negative.

Since we're allowed to talk with classmates about take-home exams, I got online to talk with a friend from class, who also goes to good ol' SHU. Beth has been getting some killer grades like 108/100 in class. She sits beside me, and she's better at math than she thinks she it.

Here's the actual word problem:

A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours to prepare, 2 hours to paint, and 9 hours to fire. A tree takes 17 hours to prepare, 3 hours to paint, and 4 hours to fire. A sleigh takes 4 hours to prepare, 14 hours to paint and 7 hours to fire. If the workshop has 120 hours prep time, 61 hours for painting, and 115 hours for firing, how many of each can be made?

Read on for the crazy antics towards the solution--which does work out. I got it! Excuse the lowercase and slang--this is direct from the IM conversation for authenticity :-)

me: hey ya

Beth: BAH! hiya... ><

me: you're working on math, too??

Beth: the ceramics problem. i keep messing it up

Beth: did you get that one?

me: yep. i got some weird answer with like 15507/1517 as x. not answers.

Beth: i keep getting negative numbers

me: nope... it doesn't work with my answers...

me: ah ha.

me: i started out making a table like we did in class.

me: but i dunno if i made it correctly... so that may be where the problem lies.

Beth: i dunno whatswrong. i did too

me: gahhhh

Beth: well what are your variables and then what are your equations?

me: okay, my equations were like this:

me: 3x + 17y + 4z = 120

me: 2x + 3y + 14z = 61

me: 9x + 4y + 7z = 115

Beth: ok so i did 1 and 3 linear combination.

me: yeah, i did linear combo too.

me: i took the 2nd eq. and the 3rd eq. but M(-2) for the 3rd.

Beth: k and i got -47t -5s = -245

me: so that got rid of z.

Beth: aww lol i got rid of w or x

me: ah ha. we definetly did this differently. that's okay.

Beth: so then did 1 and 3 and then solved my #4 equation for s or z

me: so we have the same equations, correct?

Beth: then subbed back in. yup

me: (we set 'em up right from the chart, then?)

Beth: yeah i'm pretty sure.

me: 'cause if anywhere, that's where i thought i could've screwed up

Beth: got t or y is equal to -2089(-5/1723)

me: eesh, that sure is an ugly number.

Beth: which works out to roughly 6.0621

me: eww

Beth: so i figured um.. round it?

me: nah, i didn't get anything like that ><

Beth: rats. what'd you get?

me: okay

me: got rid of z with eq. 2 and 3. then did 1 and 3 to get rid of z again... ended up wth these: -14x - 5y = -169 and -15x + 103y = 380

me: so then i did the derivative thing

me: got x = 15507/1517, y = 7855/1517

me: and then used those ugly things to get z = (about) 1.787

me: ewwwwwwwww.

Beth: rwar. ok wait. i'm trying this again doing it alittle different

me: okay me too

Beth: the way i did it befroe my x term was a -134

Beth: what the heck

me: seriously!

me: they're going to throw away 134 wreaths.

me: just pitch 'em.

Beth: lol or you have to give them to them

Beth: hmph.

me: lol!

me: the numbers are what's not pretty. having 17 and 14 to deal with, and those weird constants on the other side of = is awful.

Beth: yah

me: i'm thinking about taking eq. 2 M(4) and eq. 3 M(3) to get rid of y first...

me: whatcha think 'bout that?

me: i mean eq. 3 M(-3) to get rid of the ys

Beth: well i'm trying the x again, just in a different way. i mean that sounds as good as any other lol

me: kk

me: nooooooooo! i can't get rid of the 17y... 17 is prime. i can't use 3 or 4 to get 17.

me: damn.

me: back to the drawing board.

Beth: haha i didn't even think of that

me: so the ys must stay.

me: i got the same eq. for one that you did --- -47y - 5z = -245

me: the other is -16y + 34z = -57

Beth: hm i got -25t +34s=-423

Beth: i did 1, 3 and then 1, 2

me: well, i used thoes same ones.

Beth: 1 * -2

Beth: 2 *3

me: yeah.

Beth: lolo

me: k, how'd i mess that up

Beth: -34 plus 9?

me: naw, there's one problem solved.

me: ok, so we each had part of it right?

me: *phew*

Beth: haha together we make 1 complete mathmatician

me: indeed...

Beth: you try combining those 4 and 5 eq we got?

me: i'm working on using the derivative thingy

Beth: ah k

me: Ds = -1723?

me: ok

me: 8615/1723 for y

me: 3446/1723 for z

me: icky.

me: y=5!!!

me: it's divisible!!!

me: wow!!!

me: z=2!!!!!

Beth: how the hell did you do that????

me: yes yes yes!

me: I HAVE NO CLUE!!!!

me: lol!!!!

Beth: haha

me: ok

me: maybe i do

Beth: k go slow

me: here-- use the derivative thing

Beth: k

me: equations: 4) -47y -5z = -245

me: 5) -25y + 34z = -57

Beth: k

me: ok

me: so using the derivative format, -47*34=-1598

me: and -25*5=125

me: so -1598 - 125 = -1723 (this is Ds)

me: then...

me: for Dy

me: -245*34 = -8330

Beth: yup

me: and -57*-5 = 285

me: so -8330 - 285 = -8615

me: that's Dy

me: ready for Dz?

me: -47*-57 = 2679

me: -25*-245 = 6125

me: so 2679 - 6125 = -3446

Beth: yup

me: yay!

me: Dy/Ds = -8615/1723 = 5 !!!

Beth: holy crap

me: Dz/Ds = -3446/-1723 = 2 !!!

me: yay!

me: i'm so excited!!!

Beth: ok my brain hurts.

Beth: hehe

me: me too..

Beth: why wouldn't it work the other ways though????

me: and x = 9

me: i used #1 to put the y and z in

*me: i'm so proud i feel like blogging this...*

me: *geek attack!!!*

*** Auto-response from sephim64: karissa kilgore is my hero!

Beth: hehe

me: HAHA!

me: you're a riot!

me: i love it.

Beth: i try :D

Posted by KarissaKilgore at June 22, 2005 9:23 PM