math

If I give you $40 then the ratio of my money to yours is 4 : 5. On

the other hand, if you give me $40, then the ratio is 8 : 1. How

much money do both of us have? please show all steps

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  1. 4:5 = 40:50

    8:1 = 80:10

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    Ms. Sue
  2. Let the money you have be "x" and what your friend has be "y."

    In first case,

    x:(y+40) = 4:5
    5x = 4(y+40)
    5x = 4y + 160
    x = (4y+160)/5 ----- equation (i)

    In second case,

    (x+40):y = 8:1
    x+40 = 8y
    x = 9y-40
    (4y+160)/5 = 8y-40 [from equation (i)]
    4y+160 = 40y-200
    160+200 = 40y-4y
    360 = 36y
    y = 10.

    Applying the above obtained value of y in equation (i). We have,

    x = [(4*10)+160]/5
    x = (40+160)/5
    x = 200 / 5
    x = 40.

    So you have $40 whereas your friend has $10.

    (The reason why I supplemented Ms. Sue's answer is because I believed the question is asking for the initial amount of money both had, not after passing money along to the other.)

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