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Math Help - Challenging grade 6 question or grade 9 ?

  1. #1
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    Challenging grade 6 question or grade 9 ?

    Abel, Bob, Conan, Dave and Elijah divided a certain number of marbles amongst themselves in the following way: Abel took 1 marble and 20% of the remaining marbles, then Bob took 1 marble and 20% of the remaining marbles. Conan, Dave and Elijah did the same. At least how many marbles were there in tbe beginning?

    I have two answers but do not know which is correct. Is it a matter of how you interpret the 20% of the remaining ? Math is meant to be black and white but when different ppl say different things ... confusing


    3121 and 10

    Answer 1
    [1][ ][ ][ ][ ][ ] --> 1 + 5/4 (1 + 5/4 (1 + 5/4 (1 + 5/4 (1 + R))))) units not drawn to scale
    [1][ ][ ][ ][ ][ ] --> 1 + 5/4 (1 + 5/4 (1 + 5/4 (1 + R)))) units not drawn to scale
    [1][ ][ ][ ][ ][ ] --> 1 + 5/4 (1 + 5/4 (1 + R)) units not drawn to scale

    [1][ ][ ][ ][ ][ ] --> 1 + 5/4 (1 + R)
    [1][][][][][] --> 1 + R

    As R is a multiple of 5, try till you get the first expression as a whole number. Solve using Microsoft Office - Excel, the first whole number is 3121.

    There were 3121 marbles in the beginning.

    Answer 2
    each person has 1 marble plus 20% of the 'remainder'
    --> There are 5 marbles + 5x20% of the 'remainder'
    --> 100% of the remainder is used / split across the 5 people

    So, what is the smallest number that satisfies these conditions
    - 100% of the Remainder / 5 is a positive whole number (cannot have a fraction of a marble nor a negative marble)
    - the Remainder is greater than zero. If not than, 0/5 = 0 producing a whole number. I don't think they are looking for this answer however. I would think that the Remainder needs to be greater than 0. With this assumption, the Remainder needs to be a multiple of 5.

    The smallest multiple of 5 is 5.
    --> 5 marbles + 5 marbles = 10 marbles

    The smallest number of marbles is 10.
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  2. #2
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    i think it wants answer 1 as well.

    edit typo fixed
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  3. #3
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    Hello spaarky

    Your first answer is correct: the lowest number you can start with is 3121. This leaves 1020 marbles at the end, which is 4^5-4. In fact, all solutions will leave a number of marbles in the form 4^5n-4,\;n=1,\; 2,\; 3,\; ... I'll leave it to someone else (or you!) to prove it!

    Grandad
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