document.write( "Question 1041077: A man's age is three times the sum of the age of his two sons, one of whom is twice as old as the other; in 12 years the sum of the son's ages will be three-fourths of their father's age. Find their respective ages. \n" ); document.write( "
Algebra.Com's Answer #656014 by josgarithmetic(39617)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Father's Age              y\r\n" );
document.write( "A Son's Age               b\r\n" );
document.write( "The Other Son's Age       s\r\n" );
document.write( "

\n" ); document.write( "Follow the written description closely and translate into equations.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"system%28y=3%28b%2Bs%29%2Cs=2b%2C%28b%2B12%29%2B%28s%2B12%29=%283%2F4%29%28y%2B12%29%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Solve the system. FORMING the system of equations is the biggest part of the solution to the given problem description.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"y=3%28b%2B2b%29\"
\n" ); document.write( "\"y=9b\"
\n" ); document.write( "-
\n" ); document.write( "\"b%2Bs%2B24=%283%2F4%29%28y%2B12%29\"
\n" ); document.write( "\"4b%2B4s%2B72=3y%2B36\"
\n" ); document.write( "\"4b%2B4s%2B36=3y\"
\n" ); document.write( "-
\n" ); document.write( "\"4b%2B4%2A2b%2B36=3y\"
\n" ); document.write( "\"12b%2B36=3y\"
\n" ); document.write( "\"4b%2B12=y\"
\n" ); document.write( "-
\n" ); document.write( "Simpler System, \"system%284b%2B12=y%2Cy=9b%29\"
\n" ); document.write( "-
\n" ); document.write( "Simple substitution for y, OR simply equating expressions for y,
\n" ); document.write( "\"4b%2B12=9b\"
\n" ); document.write( "\"12=5b\"
\n" ); document.write( "\"b=12%2F5=2%262%2F5\"-----------this suggests that I made a mistake, because we usually expect Natural numbers for this kinds of age description exercises. You can keep working with it, or recheck my steps.
\n" ); document.write( "
\n" );