augmented matrixes.

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Feb 5th 2011, 06:29 PM
Almondzqueen

augmented matrixes.

a real estate developer is planning to build a new apartment complex consisting of one -bedroom aunits and two -and three - bedroom townhouses. a total of 192 units are planned and the number of family units two and three bedroom townhouses will equal the number of one bedroom units. If the number of one bedroom units will be 3 times the number of three bedroom units find how many units of each type will be in the complex

...Ok so I came up with this:
1x + 2y + 3z = 192
1x - 1y - 1z = 0
1x - 0 - 3z = 0

I am not sure if this is correct. At the end, when it is worked out, the numbers don't seem to fit. I cannot figure out what I am doing wrong. Perhaps it is 1x - 0 + 3z =0?
Need some Help? Appreciate it.
Feb 5th 2011, 06:48 PM
Prove It

First of all, what are you using $\displaystyle x,y,z$ to represent?
Feb 5th 2011, 07:02 PM
Almondzqueen

x= 1 bedroom townouse
y= 2 bedrm townhouse
z= 3 bedrm townhouse
Feb 5th 2011, 07:07 PM
Prove It

Your equations should be:

A total of 192 units are to be built:
$\displaystyle x + y + z = 192$

The number of two and three bedroom townhouses will equal the number of one bedroom units:
$\displaystyle x = y + z$

The number of one bedroom units is three times the number of three bedroom units
$\displaystyle x = 3z$ .

Solve these equations simultaneously.
Feb 5th 2011, 07:14 PM
Almondzqueen

My professor wants Gauss-Jordan method and that's why I think I am getting stuck a little more. I am just getting used to it.
Feb 5th 2011, 08:09 PM
CaptainBlack

Quote:

Originally Posted by Almondzqueen

My professor wants Gauss-Jordan method and that's why I think I am getting stuck a little more. I am just getting used to it.

So does that mean you need more help?

The augmented matrix is:

$\left[ \begin{array}{rrr|r}<br /> 1&1&1&192 \\<br /> 1&-1&-1&0 \\<br /> 1&0&-3&0 \end{array} \right]$

(you may not have been taught to use a vertical separator between the coefficients and the right hand sides so you may ignore it if you wish)

CB
Feb 5th 2011, 08:11 PM
Prove It

Quote:

Originally Posted by Almondzqueen

My professor wants Gauss-Jordan method and that's why I think I am getting stuck a little more. I am just getting used to it.

Now that you know the correct equations you should be able to set up the correct augmented matrix.