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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


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