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Math Help - Alegbra/Logic Question

  1. #1
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    Alegbra/Logic Question

    There are 29 students in Miss Spelling’s class. As a special holiday gift, she bought each of them chocolate letters with which they can spell their names. Unfortunately, some letters cost more than others — for instance, the letter A, which is in high demand, is rather pricey; whereas the letter Q, which almost no one wants, is relatively inexpensive. The price of the chocolate letters for each student in her class is shown in the table below.

    AIDEN – 386 ARI – 209 ARIEL – 376 BLAIRE – 390 CHARLES – 457
    CLARE – 334 DEAN – 317 EARL – 307 FRIDA – 273 GABRIEL – 410
    IVY – 97 KOLE – 249 LEIA – 317 LEO – 242 MAVIS – 246
    NADINE – 453 NED – 236 PAUL – 167 QASIM – 238 RACHEL – 394
    RAFI – 231 SAM – 168 TIRA – 299 ULA – 148 VERA – 276
    VIJAY – 179 WOLKE – 272 XAVIER – 346 ZERACH – 355

    How much would it cost to buy the letters in the name 'Morrissey'?
    Last edited by Broadleaf; March 5th 2014 at 02:44 PM.
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  2. #2
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    Re: Alegbra/Logic Question

    This is a very time consuming kind of problem. I shall show you how to start

    From the names Earl and Ariel, we can see see that they share the following letters A, E, R, and L. And the letters for Earl cost 307 and those for Ariel cost 376

    So E + A + R + L = A + E + L + R = 307

    And A + R + I + E + L = (A + E + L + R) + I = 376

    But that means 307 + I = 376 so I = 376 - 307 = 69.

    Do you see how to proceed?
    Thanks from mash and Broadleaf
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  3. #3
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    Re: Alegbra/Logic Question

    dump all of this into matrix equation and solve it. For example AIDEN gets you

    A + I + D + E + N = 386 so the first row of your matrix is

    1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0

    and of course the right hand side column is just the prices associated with each name (row).

    If the problem is well posed you can solve it using row reduction or what have you.
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  4. #4
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    Re: Alegbra/Logic Question

    Thank you both.
    I am only in year eight so I do not quite have a grasp on the solution provided by romsek, but JeffM was easily understandable.
    Thanks for helping me out!
    ~Broadleaf
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  5. #5
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    Re: Alegbra/Logic Question

    Hello, Broadleaf!

    There are 29 students in Miss Spelling’s class. As a special holiday gift, she bought each of them chocolate letters
    with which they can spell their names. Unfortunately, some letters cost more than others. For instance, the letter A,
    which is in high demand, is rather pricey; whereas the letter Q, which almost no one wants, is relatively inexpensive.
    The price of the chocolate letters for each student in her class is shown in the table below.

    AIDEN – 386 ARI – 209 ARIEL – 376 BLAIRE – 390 CHARLES – 457
    CLARE – 334 DEAN – 317 EARL – 307 FRIDA – 273 GABRIEL – 410
    IVY – 97 KOLE – 249 LEIA – 317 LEO – 242 MAVIS – 246
    NADINE – 453 NED – 236 PAUL – 167 QASIM – 238 RACHEL – 394
    RAFI – 231 SAM – 168 TIRA – 299 ULA – 148 VERA – 276
    VIJAY – 179 WOLKE – 272 XAVIER – 346 ZERACH – 355

    How much would it cost to buy the letters in the name MORRISSEY?

    Like JeffM, I found some values by subtraction.

    . . \begin{array}{ccc} AIDEN &=& 386 \\ DEAN &=& 317 \\ \hline \end{array}
    . . . . . . . I \;\;\;\,=\;\;\;69

    . . \begin{array}{ccc} ARIEL &=& 376 \\ LEIA &=& 317 \\ \hline \end{array}
    . . . . . . R \;\;\;\,=\;\;\;59

    . . \begin{array}{ccc} CHARLES &=& 457 \\ RACHEL &=& 394 \\ \hline \end{array}
    . . . . . . . . . S \;\;\;\,=\;\;\;63


    I'll let you find the values for E, M, O, and Y.
    Thanks from Broadleaf
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  6. #6
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    Re: Alegbra/Logic Question

    very clever, the names seem to be chosen with this sort of thing in mind
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