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Alan, Benjamin and Charles shared a bag of toy blocks. Benjamin took 3/5 as many toy blocks as Charles. Alan took twice as many toy block as the total Benjamin and Charles took. After Alan had given 20 to Benjamin and 4 to Charles, Benjamin gave 5 to Charles. In the end, all three of them had the same number of toy blocks. Find the difference between the number of toy blocks that Alan and Benjamin had at first.

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  1. Let the no. of toy blocks Alan has be ‘a’
    Let the no. of toy blocks Benjamin has be ‘b’
    Let the no. of toy blocks Charles has be ‘c’
    Given: b = 3/5c
    a = 2 (b + c)
    a - 20 - 4 = b + 20 - 5 = c + 4 + 5
    a - 24 = 3/5c + 15 = c + 9
    Solving, 3/5c + 15 = c + 9
    15 - 9 = c - 3/5c
    3 = c/5
    c = 15

    Therefore, b = 3 * 3 = 9
    b = 9
    a = 2(9 + 15) = 48
    Difference number of toy blocks that Alan and Benjamin had at first = a - b = 39

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