document.write( "Question 557603: A two-digit number is eight times the sum of its digit. When the number is added to the number obtained by reversing the digits, the sum is 99. Find the original number.
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Algebra.Com's Answer #362706 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Let x = the 10's digit
\n" ); document.write( "Let y = the units
\n" ); document.write( "then
\n" ); document.write( "10x+y = the two-digit number
\n" ); document.write( ":
\n" ); document.write( "A two-digit number is eight times the sum of its digit.
\n" ); document.write( "10x + y = 8(x + y)
\n" ); document.write( "10x + y = 8x + 8y
\n" ); document.write( "10x - 8x + y - 8y = 0
\n" ); document.write( "2x - 7y = 0
\n" ); document.write( ":
\n" ); document.write( " When the number is added to the number obtained by reversing the digits, the sum is 99. Find the original number.
\n" ); document.write( "10x+y + 10y+x = 99
\n" ); document.write( "11x + 11y = 99
\n" ); document.write( "simplify, divide by 11
\n" ); document.write( "x + y = 9
\n" ); document.write( "Multiply this equation by 2, subtract the 1st equation
\n" ); document.write( "2x + 2y = 18
\n" ); document.write( "2x - 7y = 0
\n" ); document.write( "-------------subtraction eliminates x, find y
\n" ); document.write( "9y = 18
\n" ); document.write( "y = 2
\n" ); document.write( "then
\n" ); document.write( "x + 2 = 9
\n" ); document.write( "x = 7
\n" ); document.write( ":
\n" ); document.write( "72 is the number, you can check this in both statement equations:
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