document.write( "Question 1016873: a+(1/(b+1/c)=37/16\r
\n" ); document.write( "\n" ); document.write( "find a,b and c if a,b and c are positive integers \n" ); document.write( "
Algebra.Com's Answer #633254 by robertb(5830)\"\" \"About 
You can put this solution on YOUR website!
\"a%2B1%2F%28b%2B1%2Fc%29=37%2F16\"\r
\n" ); document.write( "\n" ); document.write( "Upon reduction, the left-hand side becomes \"%28a%2Babc%2Bc%29%2F%281%2Bbc%29\"
\n" ); document.write( "We can let 1 + bc = 16, or bc = 15. (Assuming the top and bottom are relatively prime.)\r
\n" ); document.write( "\n" ); document.write( "==>a + abc + c = a + 15a +c = 16a + c = 37.\r
\n" ); document.write( "\n" ); document.write( "Since b and c are positive integers, the only possibilities for b and c are as follows:\r
\n" ); document.write( "\n" ); document.write( "b = 1, c = 15
\n" ); document.write( "b = 3, c = 5
\n" ); document.write( "b = 5, c = 3
\n" ); document.write( "b = 15, c = 1\r
\n" ); document.write( "\n" ); document.write( "From 16a + c = 37, only the value c = 5 will give a positive integer value of a = 2. Therefore, a = 2, b = 3, and c = 5.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );