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Setting up a matrix with word problems

  1. Jan 24, 2013 #1
    1. The problem statement, all variables and given/known data

    A florist offers three sizes of flower arrangements containing roses, daisies,
    and chrysanthemums.
    Each small arrangement contains one rose, three daisies, and three chrysanthemums.
    Each medium arrangement contains two roses, four daisies, and six chrysanthemums.
    Each large arrangement contains four roses, eight daisies, and six chrysanthemums.
    One day, the florist noted that she used a total of 24 roses, 50 daisies, and 48 chrysanthemums in filling orders for these three types of arrangements.
    How many arrangements of each type did she make?

    I'm sort of confused on how to set these equations up... like what do they = to?
    Let x = roses, y = daises, z = chrysanthemums

    Small arrangement: 1x + 3y + 3z = ??
    Medium arrangement: 2x + 4y + 6z = ??
    Large arrangement: 4x + 8y + 6z = ??
    Restriction: 24x + 50y + 48z = ??

    Im not sure what these equal to. If I could figure that out maybe I could set a matrice and solve..
     
  2. jcsd
  3. Jan 24, 2013 #2

    Dick

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    Homework Helper

    Why don't you back up a bit? Put x, y and z to be the things you actually want to solve for. Let x=number of small arrangements, y=number of medium arrangements and z=number of large arrangements. What equations do you get then?
     
  4. Jan 24, 2013 #3
    ok starting simple.. how do I break down the roses, daisies, and chrysanthemums in the small arrangement which is "x"? Like how would I denote each of these three.
     
  5. Jan 24, 2013 #4

    Dick

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    Each small contains 1 rose, each medium contains 2 roses, each large contains 4 roses. What are the number of total roses in terms of x, y and z? You know the total is 24, right? What equation does that give you? Choosing the variable x to be the number of roses is useless. You already know the total number of roses.
     
  6. Jan 24, 2013 #5
    Ok I got the answer. Thank you!
     
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