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Matrices Word Problem help needed

  1. Sep 4, 2008 #1
    1. The problem statement, all variables and given/known data
    Any help would be greatly appreciated! I have to use matrices to figure these out.

    1. A retired couple wishes to invest $150,000, diversifying the investment in three areas: a high-risk stock with an expected rate of return of 15%, a low risk stock with an expected rate of return of 10%, and government bonds at 8% return. To protect their investment, they wish wish to place twice as much money in the low-risk stock as the high risk stock and use the remainder to buy bonds. How should the money be allocated per investment to yield a total profit of $17,500 return on their investment?

    2. Three solutions contain a certain acid. The first contains 10% acid, the second 30% , and the third 50%. A chemist wishes to use all three solutions to obtain a 40-liter mixture containing 35% acid. If the chemist wants to use twice as much of the 50% solution as of the 30% solution, how many liters of each solution should be used?

    All I need help with is getting these bad boys started and I can go from there.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 5, 2008 #2
    hmm, I'm not sure how to represent matrices in this window. I have a stab at helping out anyway. This is a general formula.

    | percentage A | |amount of A |
    | | | |
    | percentage B | . |amount of B | = pA*aA + pB*aB + pC*aC
    | | | |
    | percentage C | |amount of C|


    Remember, the amount of something multiplied by how much that something contains of a desired substance gives you how much of the desired substance you have in total.
     
  4. Sep 5, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Let the amount invested at 15% be x, the amount invested at 10% be y, and the amount invested at 8% be z. Then, "A retired couple wishes to invest $150,000" so x+ y+ z= 150000. "To protect their investment, they wish wish to place twice as much money in the low-risk stock as the high risk stock and use the remainder to buy bonds" so y= 2x or 2x- y= 0. "How should the money be allocated per investment to yield a total profit of $17,500 return," so .15x+ .10y+ .08z= 17500. Do you know how to write the equations
    x+ y+ z= 150000
    2x- y = 0
    .15x+ .10y+ .08z= 17500
    as a matrix multiplication?

    Let x be the amount of the 10% acid solution, y the amount of the 30% solution, and z the mount of the 50% acid solution.

    "A chemist wishes to use all three solutions to obtain a 40-liter mixture containing 35% acidA chemist wishes to use all three solutions to obtain a 40-liter mixture containing 35% acid" tells us two things: x+ y+ z= 40 and .10x+ .30y+ .50z= .35(40). "the chemist wants to use twice as much of the 50% solution as of the 30% solution" tells us z= 2y or 2y- z= 0.

    Can you write
    x+ y+ z= 40
    .10+ .30y+ .50z= .35(40)= 14
    2y- z= 0
    as a matrix multipllication?

    [quolte]All I need help with is getting these bad boys started and I can go from there.

    2. Relevant equations



    3. The attempt at a solution[/QUOTE]
     
  5. Sep 5, 2008 #4
    Thank you very much ... you're the greatest!!!
     
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