document.write( "Question 722277: The product of a two-digit number and the same number with its digits reversed is 3154. Find the sum of the two numbers. \n" ); document.write( "
Algebra.Com's Answer #442720 by ankor@dixie-net.com(22740)\"\" \"About 
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The product of a two-digit number and the same number with its digits reversed is 3154.
\n" ); document.write( " Find the sum of the two numbers.
\n" ); document.write( "We only have one equation and two unknown
\n" ); document.write( ":
\n" ); document.write( "let a = the 10's of the original equation
\n" ); document.write( "let b = the units
\n" ); document.write( ":
\n" ); document.write( "the sum:
\n" ); document.write( "s = (10a + b)+ (10b + a)
\n" ); document.write( "s = 11a + 11b
\n" ); document.write( "s = assume the sum will be a multiple of 11,
\n" ); document.write( ":
\n" ); document.write( "see if that works:
\n" ); document.write( "Let n = one of the numbers, we know that the difference between numbers that are reversed are multiple of 9, after some hit and miss came up with an equation with an integer solution:
\n" ); document.write( ":
\n" ); document.write( "n(n+45) = 3154
\n" ); document.write( "n^2 + 45n - 3154 = 0
\n" ); document.write( "solve for n
\n" ); document.write( "n = 38, then 83 is the other number
\n" ); document.write( "Check
\n" ); document.write( "38 * 83 = 3154
\n" ); document.write( "and
\n" ); document.write( "38 + 83 = 121 is the sum \n" ); document.write( "
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