document.write( "Question 640694: the sum of the digit of a three-place number is 16. if the digit are reversed and the resulting number added to the original number the sum is 1049. if the resulting number is subtracted from the original number the difference is 297. what is the number? \n" ); document.write( "
Algebra.Com's Answer #403415 by ankor@dixie-net.com(22740)\"\" \"About 
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The three digits; x, y, z
\n" ); document.write( "then
\n" ); document.write( "100x+10y+z = \"the original number\"
\n" ); document.write( ":
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "\"the sum of the digit of a three-place number is 16.\"
\n" ); document.write( "x + y + z = 16
\n" ); document.write( ":
\n" ); document.write( "\"if the digit are reversed and the resulting number added to the original
\n" ); document.write( " number the sum is 1049.\"
\n" ); document.write( "(100x + 10y + z) + (100z + 10y + x) = 1049
\n" ); document.write( "Combine like terms
\n" ); document.write( "100x + x + 10y + 10y + 100z + z = 1049
\n" ); document.write( "101x + 20y + 101z = 1049
\n" ); document.write( "
\n" ); document.write( "\"if the resulting number is subtracted from the original number the difference
\n" ); document.write( " is 297.\"
\n" ); document.write( "(100x + 10y + z) - (100z + 10y + x) = 297
\n" ); document.write( "100x + 10y + z - 100z - 10y - x = 297
\n" ); document.write( "100x - x + 10y - 10y + z - 100z = 297
\n" ); document.write( "99x - 99z = 297
\n" ); document.write( "Simplify divide by 99
\n" ); document.write( "x - z = 3
\n" ); document.write( ":
\n" ); document.write( "Multiply the 1st equation by 101 and subtract the 2nd equation
\n" ); document.write( "101x + 101y + 101z = 1616
\n" ); document.write( "101x + 20y + 101z = 1049
\n" ); document.write( "---------------------------Subtraction eliminates x and z, find y
\n" ); document.write( " 0 + 81y + 0 = 567
\n" ); document.write( "y = \"567%2F81\"
\n" ); document.write( "y = 7
\n" ); document.write( ":
\n" ); document.write( "Back to the 1st equation, replace y with 7
\n" ); document.write( "x + 7 + z = 16
\n" ); document.write( "x + z = 9; subtracted 7 from both sides
\n" ); document.write( "then
\n" ); document.write( "x + z = 9
\n" ); document.write( "x - z = 3
\n" ); document.write( "------------addition eliminates z, find x
\n" ); document.write( "2x = 12
\n" ); document.write( "x = 6
\n" ); document.write( "then we know x + z = 9
\n" ); document.write( "6 + z = 9
\n" ); document.write( "z = 3
\n" ); document.write( ":
\n" ); document.write( "original number: 673
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Confirm this in the statement:
\n" ); document.write( "\"the resulting number is subtracted from the original number the difference
\n" ); document.write( " is 297.\"\
\n" ); document.write( "673 - 376 = 297\r
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