document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #635453 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4242=k%2814%2Bm%2F50%29\"$
\n" ); document.write( "

\r\n" );
document.write( "Solve that for k and simplify, get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "k is an integer, so the denominator m+700\r\n" );
document.write( "must divide evenly into 212100.\r\n" );
document.write( "\r\n" );
document.write( "We are looking for a factor of 212100 that\r\n" );
document.write( "is the number m greater than 700.\r\n" );
document.write( "\r\n" );
document.write( "212100's prime factorization is 2²∙5²∙3∙7∙101\r\n" );
document.write( "\r\n" );
document.write( "Looking at those prime factors, we see that\r\n" );
document.write( "when we multiply the last two together, we\r\n" );
document.write( "get 7∙101 = 707. That is the next factor of \r\n" );
document.write( "212100 greater than 700. So if we take m=7\r\n" );
document.write( "the denominator m+700 will be 707.\r\n" );
document.write( "\r\n" );
document.write( "So we take  and \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer: k = 300, m = 7, so k+m = 307 \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );