MATRIX

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JOSH BAR

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Sep 29, 2009
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A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth & Sons (SSS), and Bagel's Best Friend Co. (BBF). One month, the total order of cheese came to 100 tons (they do a booming trade). The costs were $80, $50 and $65 per ton from the three suppliers respectively, with the total cost amounting to $6,125. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier?
Cheesy Cream Corp. 1_____tons
Super Smooth & Sons 2 _____tons
Bagel's Best Friend Co. 3 ______tons

By setting this up, I get

x+y+z=100
80x+50y+65z=6125
x=z

How do you set up the matrix?
 
JOSH BAR said:
A bagel store orders cream cheese from three suppliers, Cheesy Cream Corp. (CCC), Super Smooth & Sons (SSS), and Bagel's Best Friend Co. (BBF). One month, the total order of cheese came to 100 tons (they do a booming trade). The costs were $80, $50 and $65 per ton from the three suppliers respectively, with the total cost amounting to $6,125. Given that the store ordered the same amount from CCC and BBF, how many tons of cream cheese were ordered from each supplier?
Cheesy Cream Corp. 1_____tons
Super Smooth & Sons 2 _____tons
Bagel's Best Friend Co. 3 ______tons

By setting this up, I get

x+y+z=100
80x+50y+65z=6125
x=z

How do you set up the matrix?
Click to expand...

1 * x + 1 * y + 1 * z = 100
80*x + 50*y + 65* z = 6125
1 * x + 0 * y + (-1)z = 0
 
JOSH BAR said:
I did this and got

x=75
y=100
z=-75

It is surely wrong.

you got

x = -z ( = 75)

However, you were given

x = z


but it was counted wrong on my answers
Click to expand...
 
I got the answers through guessing, but how do I go it algebraically.

x=25
y=50
z=25
 
By solving the matrix

What have you been taught to apply in such case (may be Gauss-Jordan elimination)?
 
I have been taught to manipulate the rows to get the 1s in a diagnol pattern, but when I do the solutions are not the answers.
 
Must be doing something wrong - cannot tell without seeing YOUR work.
 
\(\displaystyle 1 \ \ \ \ 1 \ \ \ \ 1 \ \ \ \ \ \ 100 \ \ \ \ \ \ \ \ \ \ \ \ \ 1 \ \ \ 0 \ \ \ 0 \ \ \ 25\)

\(\displaystyle 80 \ \ \ 50 \ \ \ 65 \ \ \ 6125 \ \ \ = \ \ \ \ \ 0 \ \ \ 1 \ \ \ 0 \ \ \ 50\)

\(\displaystyle 1 \ \ \ 0 \ \ \ -1 \ \ \ \ 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0 \ \ \ 0 \ \ \ 1 \ \ \ 25\)

Got it. If you have a TI-89, use rref and avoid the grunt work.
 
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