6th grade math

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A chocolate bar is separated into several equal pieces. If one person eats 1/4 of the pieces, and a second person eats 1/2 of the remaining pieces, there are six pieces left over. Into how many pieces was the original bar divided?

  • 6th grade math -

    1 - 3/4 = 1/4

    1/4 = 6 pieces

    4 * 6 = 24

    Let's see if that works --

    6 + 12 + 6 = 24

    Yep, it works!

  • 6th grade math -

    let the number of pieces be x

    (1/4)x + (1/2)(1 - (1/4)x) + 6 = x

    x/4 + 3x/8 + 6 = x
    multiply by 8

    2x + 3x + 48 = 8x
    x = 16

    check
    they eat 1/4 of 16, leaving 12
    then they eat 1/2 of that , leaving 6


    Ms Sue had 24.
    eating 1/4 of that leaves 18
    eating 1/2 of that would leave 9, not 6

  • 6th grade math -

    Here is another way to do it.
    Let x = number of pieces.
    Then x-(1/4)x -(1/2)*(3/4)x = 6
    x-(1/4)x-(3/8)x = 6
    multiply through by 8 to clear the fractions.
    8x-2x-3x=48
    3x = 48
    x = 16 pieces.
    CHECK:
    (1/4)*16 = 4 were eaten by person #1.
    That leaves 16-4 = 12 pieces.
    The second person ate 1/2 of that or (1/2)*12 = 6
    So the first person ate 4, the second person ate 6 which makes a total of 10 and that leaves 6 pieces if there were 16 initially.

  • 6th grade math -

    Oops -- thanks, Reiny.

    I didn't read very carefully. I missed the part about eating 1/2 of the REMAINING pieces.

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