Question 915218: I can't figure out how to set up this 3x3 problem, I don't need help solving.
For a party, you are cooking a large amount of stew that has meat, potatoes, and carrots. The meat cost $6 per pound, the potatoes cost $3 per pound, and the carrots cost $1 per pound. You spend $48.50 on 13.5 pounds of food. You but twice as many as carrot than potatoes.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let's define our variables. This is usually the first step.
Let
x = number of pounds of meat
y = number of pounds of potatoes
z = number of pounds of carrots
You buy "13.5 pounds of food", so x+y+z = 13.5 is your first equation
You spent $48.50 on all this food. "The meat cost $6 per pound, the potatoes cost $3 per pound, and the carrots cost $1 per pound" So the second equation is 6x+3y+1z = 48.50
When you said "You but twice as many as carrot than potatoes", I think you meant to say "you bought twice as many as carrots as potatoes". Which means
(# of carrots) = 2*(# of potatoes)
z = 2*y
=======================================================
Your three equations are
x+y+z = 13.50
6x+3y+1z = 48.50
z = 2*y
you can get the third equation into standard form to get this equivalent system
x + y + z = 13.50
6x + 3y + 1z = 48.50
0x - 2y + 1z = 0
Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html
Thanks,
Jim
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