SOLUTION: Bob is five years older than his brother Billy. The product of their ages is 414. How old are Bob and Billy.

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Question 1147216: Bob is five years older than his brother Billy. The product of their ages is 414. How old are Bob and Billy.
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

Algebra method 

    x*(x+5) = 414.


    x^2 + 5x - 414 = 0.


Solve this quadratic equation by any way you can / (you know).


Trial and error "guessing" method 


Try to guess two factors of the number 414 such that

   
    x * y = 414  and x and y  differ by 5.


414 has factors


    2  and  207

    2*3= 6 and 69

    2*3*3 = 18 and 23   <<<---===   O-o-p-s !   these factors are PERFECTLY good (!)


Check.   18*23 = 414  and  23 - 18 = 5.


ANSWER.  18 and 23 years old.

Solved.