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Check my Math?

  1. Sep 28, 2003 #1
    Question posed:
    Julia is as old as John will be when Julia is twice as old as John was when Julia's age was half the sum of their present ages.

    John is as old as Julia was when John was half the age he will be 10
    years from now.

    How old are John and Julia?
    ______________________________
    First I let x = John's present age and y = Julia's present age

    x + 10 = John's age in 10 years

    x + 10
    ------ = 1/2 of John's age in 10 years
    2

    Now, it would be helpful to know when John was (x + 10)/2. Let's say a person is 56 years old and if I want to know when was I 20, I just subtract 56 - 20 and find that I was 20, 36 years ago.
    x + 10
    So, x - ------ will tell us how many years ago John was (x + 10)/2.
    2

    How old was Julie then? Well, if I want to know how old my 42-year-old
    brother was 36 years ago, I just subtract 42 - 36 and learn that he
    was 6.
    x + 10
    So, Julie's age must have been y - (x - -------). But, if that is what
    2
    John's age is right now, we have:

    x + 10
    x = y - ( x - ------ )
    2

    I went through this same reasoning process with the rest of the
    information in the problem and came up with another equation in two
    variables. Is that right?
     
  2. jcsd
  3. Sep 29, 2003 #2
    Yes, that is right. But since this system doesn't support blanks so well, you should rather type:
    x = y - (x - (x+10)/2).

    That's the correct equation for statement (2).
    As you correctly stated, statement (1) will give another equation in x and y, and this system of 2 equations in 2 unknowns should have a unique solution.
     
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