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Math Help - Problem on ages

  1. #1
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    Problem on ages

    Help required to solve my algebra 2 homework on ages

    The sum of the ages of a father and his is 45 years. Five years ago , the product of their ages was 34. What are the ages of the father and son?
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  2. #2
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    Re: Problem on ages

    Quote Originally Posted by burgess View Post
    Help required to solve my algebra 2 homework on ages

    The sum of the ages of a father and his is 45 years. Five years ago , the product of their ages was 34. What are the ages of the father and son?
    let the age of father be $f$ and the age of the son be $s$

    from the first line

    $f+s=45$

    from the second line

    $(f-5)(s-5)=34$

    and of course the father is older than the son, i.e.

    $f>s$

    you should be able to finish from here.
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  3. #3
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    Re: Problem on ages

    x - father's age
    y - son's age

    x+y=45
    y=45-x
    (x-5)(y-5)=34
    xy-5y-5x+25=34
    x(45-x)-5(45-x)-5x=9
    45x-x2-225+5x-5x=9
    -x2+45x-234=0

    Solving this quadratic equation, x=39 and y=45-39=6

    So, father is 39 years old and son is 6 years old.
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  4. #4
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    Re: Problem on ages

    Thank you all for the detail explanations
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