document.write( "Question 1201927: please,help me solve this problem:The sum of the ages of a mother and her child is 63.if the product of their ages four years ago was 484, what is their age now?
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #836506 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "The sum of the ages of a mother and her child is 63.
\n" ); document.write( "if the product of their ages four years ago was 484, what is their age now?
\n" ); document.write( "~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "If the sum of the ages of a mother and her child is 63 now,\r\n" );
document.write( "hence, 4 years ago this sum was 63-4-4 = 55.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, 484 = (mentally) 4*121 = 2*2*11*11.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we should combine these factors to make a sum 55 from them.\r\n" );
document.write( "For example, this way works\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "       55 = 44 + 11 = (2*2*11) + 11,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "so, we can assume that 4 years ago their age was 44 and 11;  \r\n" );
document.write( "so now their ages are 44+4 = 48 (mother)  and 11+4 = 15.   ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "You may check that there no other solutions.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I leave this job to you, for your entertainment.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Another way to solve it is to write this equation for their ages 4 years ago\r\n" );
document.write( "\r\n" );
document.write( "    x*(55-x) = 484\r\n" );
document.write( "\r\n" );
document.write( "    55x - x^2 = 484\r\n" );
document.write( "\r\n" );
document.write( "    x^2 - 55x + 484 = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and then solve it using the quadratic formula or factoring, on your choice.\r\n" );
document.write( "

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

\n" );