SOLUTION: if 42 42=k(14+m/50).where k and m are positive integers.and m<50,then what is the value of k+m? answer

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Question 1019406: if 42 42=k(14+m/50).where k and m are positive integers.and m<50,then what is the value of k+m? answer
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
4242=k%2814%2Bm%2F50%29
Solve that for k and simplify, get

k=212100%2F%28m%2B700%29

k is an integer, so the denominator m+700
must divide evenly into 212100.

We are looking for a factor of 212100 that
is the number m greater than 700.

212100's prime factorization is 2²∙5²∙3∙7∙101

Looking at those prime factors, we see that
when we multiply the last two together, we
get 7∙101 = 707. That is the next factor of 
212100 greater than 700. So if we take m=7
the denominator m+700 will be 707.

So we take m=7 and 

k=212100%2F%28m%2B700%29
k=212100%2F%287%2B700%29
k=212100%2F%28707%29 
k=300

Answer: k = 300, m = 7, so k+m = 307 

Edwin