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When a woman is as old as her father is now, she will be five times as old as her son is now. By then, her son will be eight years older than she is now. The combined ages of her father and herself are 100 years. How old is her son?

  • math -

    Let the ages be woman=w, son=s, father=f.

    The first sentence f=5s.

    Now, the woman will as old as her father in f-w years. The son will then be s+f-w years old. The second sentence says that s+f-w = 8+w.

    The 3rd sentence says that w+f = 100.

    So, we have three equations, which we can start combining:

    5s+w = 100
    s+f-w = w+8

    5s + w = 100
    6s - 2w = 8
    -------------
    16s = 208

    s=13
    f = 5s = 65
    w = 100-65 = 35

    So, in 30 years, the woman will be as old as her father is now(65), and the son will be 43, which is 8 years older than she is now.

  • math -

    The number 34,459,425 is the product of several consecutive positive odd numbers. What is the greatest of these numbers?

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