document.write( "Question 151854: Please help me with this problem. I've tried working on it but all I end up with is a headache.
\n" ); document.write( "The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed. Find the original number. \n" ); document.write( "
Algebra.Com's Answer #111637 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed. Find the original number.
\n" ); document.write( ";
\n" ); document.write( "Let x = 10's digit
\n" ); document.write( "Let y = units digit
\n" ); document.write( ";
\n" ); document.write( "two digit number = 10x + y
\n" ); document.write( ":
\n" ); document.write( "Sum of digits:
\n" ); document.write( "x + y = 8
\n" ); document.write( "or
\n" ); document.write( "y = (8-x)
\n" ); document.write( ":
\n" ); document.write( "Write an equation for the statement:
\n" ); document.write( "\"If 16 is added to the original number, the result is 3 times the original number with its digits reversed.\"
\n" ); document.write( "10x + y + 16 = 3(10y + x)
\n" ); document.write( ":
\n" ); document.write( "10x + y + 16 = 30y + 3x
\n" ); document.write( ":
\n" ); document.write( "10x - 3x + 16 = 30y - y
\n" ); document.write( ":
\n" ); document.write( "7x = 29y - 16
\n" ); document.write( ":
\n" ); document.write( " Find the original number.
\n" ); document.write( ":
\n" ); document.write( "substitute (8-x) for y in the above equation
\n" ); document.write( "7x = 29(8-x) - 16
\n" ); document.write( ":
\n" ); document.write( "7x = 232 - 29x - 16
\n" ); document.write( ":
\n" ); document.write( "7x + 29x = 232 - 16
\n" ); document.write( ":
\n" ); document.write( "36x = 216
\n" ); document.write( "x = \"216%2F36\"
\n" ); document.write( "x = 6, then, of course, y = 2
\n" ); document.write( ":
\n" ); document.write( "Original number = 62
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check solution in the statement:
\n" ); document.write( "If 16 is added to the original number, the result is 3 times the original number with its digits reversed.\"
\n" ); document.write( "62 + 16 = 3(26)
\n" ); document.write( "78 = 78 \n" ); document.write( "
\n" );