document.write( "Question 1191182: The ratio of Tom’s age to Mike’s age is 8:5. 30 years later, this ratio will be 6:5. How much older is Tom than Mike? \n" ); document.write( "

Algebra.Com's Answer #822966 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The ratio of Tom’s age to Mike’s age is 8:5.
\n" ); document.write( "30 years later, this ratio will be 6:5. How much older is Tom than Mike?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Today, they are 8x (Tom) and 5x (Mike) years old, where x is the common measure of their ages.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "30 years later\r\n" );
document.write( "\r\n" );
document.write( "     = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Cross-multiply, then simplify and find x\r\n" );
document.write( "\r\n" );
document.write( "    5*(8x+30) = 6*(5x+30)\r\n" );
document.write( "\r\n" );
document.write( "    40x + 150 = 30x + 180\r\n" );
document.write( "\r\n" );
document.write( "    40x - 30x = 180 - 150\r\n" );
document.write( "\r\n" );
document.write( "        10x   =     30\r\n" );
document.write( "\r\n" );
document.write( "          x   =     30/10 = 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, Tom is 8x = 8*3 = 24 yers old;  Mike is 5*3 = 15 years old.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Tom is  24-15 = 9 years older than Mike.    ANSWER\r\n" );
document.write( "

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

\n" );