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Systems of Linear Equations

  1. Apr 18, 2012 #1
    1. The problem statement, all variables and given/known data

    A store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. The manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?


    2. Relevant equations

    x1 + y1 = k1
    x2 + y2 = k2

    3. The attempt at a solution

    x= cashews
    y= peanuts

    5x + 1.5y = 3(x+y)

    5(30) +1.5y = 3(30+y)

    150 +1.5y = 90 + 3y

    60 = 1.5y

    40 = y

    Correct answer: 22.5 pounds of peanuts


    ------
    I know this isn't probably pre-calculus, but my teacher is reviewing matrices, and this is the first section of the chapter. I usually don't have problems doing these types of problems, especially problems relating to the mixing of nuts/candies, etc. But, for some odd reason, I'm not getting the correct answer, and I think my set-up is probably wrong. I don't see another logical way to approach this question.

    Any help is greatly appreciated!
     
  2. jcsd
  3. Apr 18, 2012 #2
    Your set up and answer seem right to me. Who says the answer is 22.5 lbs?
     
  4. Apr 18, 2012 #3
    The back of the book, apparently.
     
  5. Apr 19, 2012 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    How can the "correct answer" possibly be "22.5 lbs of peanuts" when the question is "how many pounds of cashews"?
     
  6. Apr 19, 2012 #5
    Yikes!! Hallsofivy is right!
     
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