My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 22nd, 2008, 06:57 PM   #1
Newbie
 
Joined: Sep 2008

Posts: 1
Thanks: 0

Gaus Elimination Help

Ok im totally stumped because the variables got switched up on me... here is the problem

A furniture copmany makes loungers, chairs, and footstools made out of wood, fabric and stuffing. The number of units of each of these materials needed for each of the products is given in the table below. How many of each product can be made if tehre are 54 units of wood, 63 units of fabric, and 43 units of stuffing availabe?

__________Wood__Fabric__Stuffing
Lounger_____1_____2_______2
Chair_______2_____2_______1
Footstool___3_____1_______1
Kdocimo90 is offline  
 
September 22nd, 2008, 07:24 PM   #2
Senior Member
 
Joined: Oct 2007
From: Chicago

Posts: 1,701
Thanks: 3

Re: Gaus Elimination Help

Our unknowns are: how many of each type of chair can be made. So let # of loungers = l, # of chairs = c, and # of footstools = f.

Look at the amount of wood used first; there are 54 total units, and the table says how much each product uses:
54 = l+2c+3f

And the same with fabric:
63 = 2l+2c+f

and stuffing:
43 = 2l+c+f

Flipping the equations and putting them on top of each other gives:
l +2c+3f= 54
2l+2c+f = 63
2l +c+ f = 43

Does that help you set up the matrix? Or did you already get that far?
cknapp is offline  
September 23rd, 2008, 06:55 AM   #3
Senior Member
 
Joined: Jul 2008

Posts: 895
Thanks: 0

Re: Gaus Elimination Help

You might look at it as you do in ratio and proportion. If the absolute amount of wood used in the loungers is "l", the amount of fabric and stuffing will be in the proportions 1:2:2. So the proportion in terms of absolute amounts will be l:2l:2l. This is stating that these are the absolute amounts of materials used in building the loungers. Let's follow along with this, using those absolute amounts:

loungers w:f:s = 1:2:2 = l:2l:2l
chairs w:f:s = 2:2:1 = 2c:2c:c
stuffing w:f:s = 3:1:1 = 3f:f:f

Now, looking down vertically, the total amount of wood used is l + 2c + 3f = 54
etc...
Dave is offline  
September 23rd, 2008, 03:04 PM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 21,130
Thanks: 2339

Hi Kdocimo90, please explain what "the variables got switched up on me" means. Why were you stumped? Also, were you required to use Gaussian elimination to solve the problem?
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
elimination, gaus



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Elimination Technique SamFe Calculus 3 November 23rd, 2013 04:07 AM
Gaus-Jordan PetraLenski Linear Algebra 3 November 2nd, 2011 11:17 AM
Elimination Techniques MRKhal Algebra 2 April 2nd, 2011 02:17 AM
Subsitution or Elimination titans4ever0927 Algebra 6 November 19th, 2007 06:33 PM
Gaus Elimination Help Kdocimo90 Economics 1 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.