document.write( "Question 150667This question is from textbook
\n" ); document.write( ": The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is increased by 20 which is twice the original number. Find the original number. \n" ); document.write( "
Algebra.Com's Answer #110603 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Let x = the 10's digit
\n" ); document.write( "Let y = the units digit
\n" ); document.write( ":
\n" ); document.write( "the number = (10x + y)
\n" ); document.write( "the reversed number = (10y + x)
\n" ); document.write( "\"
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( "\"The sum of the digits of a two-digit number is 11.\"
\n" ); document.write( "x + y = 11
\n" ); document.write( "or
\n" ); document.write( "y = 11-x
\n" ); document.write( ":
\n" ); document.write( "\"When the digits are reversed, the new number is increased by 20 which is twice the original number.\"
\n" ); document.write( "(10y+x) + 20 = 2(10x+y)
\n" ); document.write( "10y + x + 20 = 20x + 2y
\n" ); document.write( "10y - 2y + x - 20x = -20
\n" ); document.write( "8y - 19x = -20
\n" ); document.write( ":
\n" ); document.write( "Find the original number.
\n" ); document.write( ";
\n" ); document.write( "Substitute (11-x) for y in the above equation:
\n" ); document.write( "8(11-x) - 19x = -20
\n" ); document.write( "88 - 8x - 19x = -20
\n" ); document.write( "-8x - 19x = 20 - 88
\n" ); document.write( "-27x = -108
\n" ); document.write( "x = \"%28-108%29%2F%28-27%29\"
\n" ); document.write( "x = +4
\n" ); document.write( ":
\n" ); document.write( "y = 11-4
\n" ); document.write( "y = 7
\n" ); document.write( ":
\n" ); document.write( "original number: 47
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check solution in the statement;
\n" ); document.write( "\"When the digits are reversed, the new number is increased by 20 which is twice the original number.\"
\n" ); document.write( "74 + 20 = 2(47); confirms our solutions\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );