document.write( "Question 209635: There is a two-digit number such that the sum of its digits is 6, while the product of the digits is 1/3 the original number. Find this number. \n" ); document.write( "
Algebra.Com's Answer #158515 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
There is a two-digit number such that the sum of its digits is 6, while the product of the digits is 1/3 the original number. Find this number.
\n" ); document.write( "--------
\n" ); document.write( "t + u = 6 (Tens digit + Units digit = 6)
\n" ); document.write( "t*u = (10t + u)/3 (the original number is 10t+u)
\n" ); document.write( "3tu = 10t + u
\n" ); document.write( "u = 6-t
\n" ); document.write( "3t(6-t) = 10t + 6-t
\n" ); document.write( "18t-3t^2 = 9t+6
\n" ); document.write( "3t^2 - 9t + 6 = 0
\n" ); document.write( "t^2 - 3t + 2 = 0
\n" ); document.write( "(t-1)*(t-2) = 0
\n" ); document.write( "t = 1, u = 5
\n" ); document.write( "t = 2, u = 4
\n" ); document.write( "--------
\n" ); document.write( "24 or 15, they both work\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );