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Math Help - Linear Equations

  1. #1
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    Linear Equations

    1) A music store specialises in three types of CDs: classical, blues and heavy metal. In one week they sold a total of 420 CDs. THey sold 10% more classical than blues while sales of heavy metal constituted 50% more than the combined sales of classical and blues CDs. How many of each type of CD did they sell?

    2) A is three times as old as B. In three years' time, B will be three times as old as C. In fifteen years' time, A will be three times as old as C. What are their present ages?

    3) Henry and Thomas Wong collect basketball cards. Henry has five sixths the number of cards that Thomas has. The Wright family also has a collection of cards. George Wright has half as many cards again as Thomas, Sally Wright has 18 less than Thomas and Zeb Wright has one third the number Thomas has.

    i: Write an expression for each child's number of cards in terms of the number Thomas has.

    ii: The Wright family owns six more cards than the Wong family. Find the number of cards each child has collected.

    So far:

    Henry = H
    Thomas = T
    George = G
    Sally = S
    Zeb = Z

    H = (5/6)T
    G = (1/2)T
    S = T - 18
    Z = (1/3)T

    (5/6)T = (1/2)T + T - 18 + (1/3)T + 6
    (5/6)T = (11/6) + 6 -18
    t = 12

    Substituting that into the previous equations for each child should give the correct number of cards, but for Sally (T - 18, 12 - 18 = -6) it returns a negative value and therefore cannot be correct.

    --------------------------------------------------------------------------------------------------------------

    Could you please point me in the right direction?

    Thanks in advance.
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  2. #2
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    Re: Linear Equations

    The Wong Family has both Henry and Thomas. So for them, you should get (5/6)T + T, which becomes (11/6)T.
    Thanks from Fratricide
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  3. #3
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    Re: Linear Equations

    So therefore...?

    (11/6)T + 18 = (11/6)T

    T = 18
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  4. #4
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    Re: Linear Equations

    Bump. Still need help with the other two.
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  5. #5
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    Re: Linear Equations

    Let the number of Blue CDs sold = x
    Thus number of Classical CDs = 10% more than Blue Cds
    = x + 10% of x = 11/10 x
    Heavy Metal CDs sold = 50% more than combined sale of Blue and Classic
    = [ x + 11/10 x ] + [ 50 % of ( x + 11/10x )]
    = 21/10 x + 21/20x = 63/20x
    But total CDs sold in a week = 420
    Thus we have: x + 11/10x + 63/20 x = 105/20x = 420
    That gives x = 80
    Thus we have number of blue CDs sold = 80, Classical CDs sold = 88 and heavy metal CDs sold = 252.
    Thanks from Fratricide
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  6. #6
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    Re: Linear Equations

    Let the age of B = x years ----- 1
    Then age of A = 3x years ----- 2
    Let the age of C = y years
    AFTER 3 YEARS
    Age of B = x + 3
    Age of C = (y + 3) years
    It is given that age of B = 3 times age of C that is:
    (x+ 3 ) = 3 ( y+3) OR 3y = x 6 --- 3
    AFTER 15 YEARS
    Age of A = 3x + 15
    Age of C = y + 15
    It is given that Age of A = 3 times Age of C That is
    3x + 15 = 3 ( y + 15) = 3y + 45 = ( x-6) + 45 [ using (3) ]
    3x + 15 = x 6 + 45 OR 2x = 24 and thus x = 12
    Hence the present age of A = 36 years,
    Present age of B = 12 years and the present age of C = 2 years
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  7. #7
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    Re: Linear Equations

    ibdutt to the rescue. Thanks heaps.
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