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anonymous
 one year ago
Mixture Problem
We didn't go over them in class but they are on the online homework =(
anonymous
 one year ago
Mixture Problem We didn't go over them in class but they are on the online homework =(

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Let P=Pounds of Peanuts, C=Pounds of Cashews, R=Pounds of Raisins. Then we can establish an equation based on the first sentence they gave us,\[\large\rm P+C+R=9\]Some amount of Peanuts, Cashews and Raisins give us a total of 9 pounds, ya? :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, that makes sense so far =)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We're going to set up another equation, this one is a little trickier. This one is based on prices.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1The peanuts cost 1.50 per pound. So the total price we pay for ALL of our peanuts is \(\large\rm 1.50P\). Where P is the number of pounds of peanuts.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Similarly, our cashews will have a total price of \(\large\rm 2.00C\) While our raisins will total \(\large\rm 1.00r\)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1They tell us that the total costs, of all the nuts, is 13 dollars. So when we total up all of these totals:\[\large\rm 1.5P+2C+1R=13\]I dropped any unnecessary 0's, hopefully that wasn't confusing.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0All right, that makes sense =)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We can actually set up one more equation! :O

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1`twice as many peanuts` as `cashews`. So the pounds of peanuts, P, should be twice as large as the pounds of cashews, C.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We can write that relationship like this: \(\large\rm P=2C\) Maybe read that as, "peanuts equals twice the cashews"

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We're going to go back and substitute this relationship into our other two equations.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Our weight equation: \[\large\rm \color{orangered}{P}+C+R=9\]Will become\[\large\rm \color{orangered}{2C}+C+R=9\] While our price equation:\[\large\rm 1.5\color{orangered}{P}+2C+1R=13\]will become\[\large\rm 1.5\color{orangered}{(2C)}+2C+1R=13\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Makes sense (Just as a side note, could this also be solved with a matrix?)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Mmm definitely. Lemme think..

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \left(\begin{array}{cccc}1 & 1 & 1 & 9\\ 1.5 & 2 & 1 & 13\end{array}\right)\]Ah sorry for slow :) I'm not really familiar with augmented matrices in latex lol Setting out our third column is a little tricky. Since \(\large\rm P=2C\), subtracting 2C from each side gives us: \(\large\rm 1P2C+0R=0\) So our matrix would be:\[\large\rm \left(\begin{array}{cccc}1 & 1 & 1 & 9\\ 1.5 & 2 & 1 & 13\\ 1 &2 & 0 & 0\end{array}\right)\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Our third row* not third column, blah typo

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay! So then the answer would be (4,2,3)? And no worries! You saved my educational life! XP

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nah wait, that's not one of the answers lol.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1It's not? Hmm, that sounds right :o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No wait, wrong problem! It is that. Lol sorry

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1such a bum... just using a matrix calculator or something? lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, a TI84. Honestly the whole substitution thing loses me every time, not that your explanation was losing me! I was just curious about the matrix because I will probably use that on my test tomorrow.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1matrices are extremely useful in real world problems :) So it's definitely not a waste of time to get comfortable with your calculator!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Cool beans! Thanks so much =)
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