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by Anonymous on February 13th, 2007

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If 8 grapefuit, 7 oranges & 3 lemons weigh the same as 3 oranges, 6 grapefruit & 6 lemons, if a grapefruit weighs 2/3 as much as a lemon & if a dozen oranges weighs 3 kilos.... How much does a lemon weigh?

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Answers. 6 helpful answers below.

  • by TheKnife V2.1 - Grandiose and Obnoxious on February 20th, 2007

    TheKnife V2.1 - Grandiose and Obnoxious

    I know I'm late on this so I don't expect any points, but I like puzzles so I did it for fun, and since nobody has actually given their method, I thought I would write it out in full so people can see how to solve these things.

    Using g for grapefruits, o for oranges and m for lemons (since the 'l' looks too much like a one), we are told -

    1) 8g + 7o + 3m = 3o + 6g + 6m
    2) g = 2m/3
    3) 12o = 3

    Straightaway we can work out o - divide both sides of equation 3 by 12 and we get o = 3/12, or 1/4kg. Then if we substitute this value into equation 1, it becomes -

    4) 8g + 3m + 7/4 = 6g + 6m + 3/4

    Since we also know that 2) g = 2m/3, we can substitute this into equation 4 as well, giving -

    5) 8(2m/3) + 3m + 7/4 = 6(2m/3) + 6m + 3/4, which simplifies to
    16m/3 + 3m + 7/4 = 12m/3 + 6m + 3/4

    Gathering all the m terms on one side of the equation and all the numeric terms on the other gives us -

    6) 1 = 5m/3, or 3 = 5m, so m = 3/5kg

    And if g = 2m/3 as equation 2 says, then g = 2/3 * 3/5 = 2/5kg.

    So that is how we reach the answers of oranges = 1/4kg (250 grams), lemons = 3/5kg (600 grams) and grapefruits = 2/5kg (400 grams).

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  • by Your Conscience on February 13th, 2007

    Your Conscience

    An orange is worth .25 kilos
    A grapefruit is worth .4 kilos
    And the lemon is .6 kilos

    i did it!!!

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  • by Piero10 on November 28th, 2008

    Piero10

    8G + 7O + 3L = 3O + 6G + 6L
    G = 2/3L
    12O = 3 Kilo
    O = 3/12 Kilo or 0.25 kilo
    So
    8G + 7(0.25) + 3L = 3(0.25) + 6G + 6L
    Then
    8(2/3L) + 1.75 + 3L = 0.75 + 6(2/3L) + 6L
    Therefore
    1 = (4L + 6L) - (5,1/3L + 3L)
    And in conclusion
    L = 1,2/3 Kilo

    Were have i gone wrong?

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  • by Kamilah on February 13th, 2007

    Kamilah

    a lemon weighs or maybe 29/27 kilos?? If that's not right I give up...

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  • by Box of Chocolates on February 13th, 2007

    Box of Chocolates

    I guess a lemon weighs 37.5 grams.
    EDIT: I guess I'm not good at guessing. Next time I will do the math.

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  • by Anonymous on February 13th, 2007

    Anonymous

    Their is an answer to this question and i must say it's not easy. designed for the experianced, those who love mathematics.

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