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Math Help - help me

  1. #1
    Junior Member
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    Feb 2006
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    help me

    can any one piz help me in solving dis puzzle

    the puzzle is there r 100 rs with me i want to buy 100 balls and the balls r
    foot ball which cost rs 15 , second cricket ball which cost rupees 1 and tennis ball which cost rs 0.25 i want the solution of how many of eachg balls i can get for the 100 rs consisting of 100 balls
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  2. #2
    MHF Contributor
    Joined
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    Quote Originally Posted by bharathlece
    can any one piz help me in solving dis puzzle

    the puzzle is there r 100 rs with me i want to buy 100 balls and the balls r
    foot ball which cost rs 15 , second cricket ball which cost rupees 1 and tennis ball which cost rs 0.25 i want the solution of how many of eachg balls i can get for the 100 rs consisting of 100 balls
    This should be easy but....

    So you have 100 rs (I assume 100 rupees).
    You want to buy 100 balls, consisting of footballs (f), cricket balls (c), and tennis balls (t).
    f costs 100rs each.
    c costs 1 rupee each.
    t costs 0.25 rupee each.

    So,
    f +c +t = 100 -------------------balls-----(1)
    f(15) +c(1) +t(0.25) = 100 -----rupees-----(2)

    That is it. No more equation to make from what are given in your question.
    So there are 3 unknowns and only two independent equations. Can be solved, maybe, but we need guessing or trial and error.

    What if you buy 1 football only?
    Then,
    f=1
    So, c +t = [100-1] = 99 ----(1a)
    And, c(1) +t(0.25) = [100 -1(15)] = 85 ----(2a)

    c +0.25t = 85 ----(2aa)
    From (1a), c = 99 -t. Substitute that into (2aa),
    99 -t +0.25t = 85
    -t +0.25t = 85 -99
    -0.75t = -14
    t = -14 / -0.75 = 18.6667 ----not whole number, so not okay.

    ------------------------------------
    What if you buy 2 footballs only?
    Then,
    f=2
    So, c +t = [100-2] = 98 ----(1b)
    And, c(1) +t(0.25) = [100 -2(15)] = 70 ----(2b)

    c +0.25t = 70 ----(2bb)
    From (1b), c = 98 -t. Substitute that into (2bb),
    98 -t +0.25t = 70
    -t +0.25t = 70 -98
    -0.75t = -28
    t = -28 / -0.75 = 37.333 ----not whole number again, so not okay.

    ------------------------------------------
    What if you buy 3 footballs?
    Then,
    f=3
    So, c +t = [100-3] = 97 ----(1d)
    And, c(1) +t(0.25) = [100 -3(15)] = 55 ----(2d)

    c +0.25t = 55 ----(2dd)
    From (1d), c = 97 -t. Substitute that into (2dd),
    97 -t +0.25t = 55
    -t +0.25t = 55 -97
    -0.75t = -42
    t = -42 / -0.75 = 56 ------ping!
    Hence, from (1d), c = 97 -56 = 41

    Therefore, you can buy 3 footballs, 41 cricket balls and 56 tennis balls. ---answer.

    ---------------------------
    Check,

    f +c +t = 100 -------------------balls-----(1)
    3 +41 +56 =? 100
    100 =? 100
    Yes, so, OK.

    f(15) +c(1) +t(0.25) = 100 -----rupees-----(2)
    3(15) +41(1) +56(0.25) =? 100
    45 +41 14 =? 100
    100 =? 100
    Yes, so, OK.
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