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Mathematics

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If A gives B $3, B will have twice as much as A. If B gives A $5, A will have twice as much as B. How much does each have? Explain clearly your working.

  • Mathematics - ,

    A now has x
    B now has y

    The wording is confusing.
    Are the consecutive transfers of money, or are they independent events

    Case1 : consecutive events

    A gives $3 to b
    A now has A-3, B has y+3
    y+3 = 2(x-3)
    y+3 = 2x - 6
    2x - y = 9 , #1

    B gives $5 to A
    A now has x-3 + 5 = x+2
    B now has y+3 - 5 = y - 2

    x+2 = 2(y-2)
    x+2 = 2y - 4
    x - 2y = -6 , #2

    #1 times 2
    ---> 4x-2y=18
    #2 --> x - 2y = -6
    subract:
    3x = 24
    x = 8
    then y = 7
    A has $8 and B has $7

    first transfer, A give $3 to B
    A has 5 , and B has 10 , Does B have twice A ? yup
    2nd transfer , B gives $5 to A
    A has 10 , B has 5, does A have twice of B ? , yup

    Case 2: independent events:
    A gives $3 to B
    y+3 = 2(x-3)
    y = 2x - 9

    B gives $5 to A
    A has x+5, B has y-5
    x+5 = 2(y-5)
    x = 2y - 10 - 5
    x = 2(2x-9) - 15
    x = 4x - 33
    -3x = -33
    x = 11
    y = 13

    This too can be verified.

    Pick your interpretation.

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