document.write( "Question 72232: the sum of the two-digit number is 11. When the number is reversed, the number is 63 less than the original number. Find the original number and show work. \n" ); document.write( "

Algebra.Com's Answer #51631 by rmromero(383) $\"\"$ $\"About$

You can put this solution on YOUR website!


\n" );
document.write( "the sum of the two-digit number is 11.  When the number is reversed, the number is 63 less than the original number.  Find the original number and show work.\r
\n" );
document.write( "\n" );
document.write( "What is asked in the problem?
\n" );
document.write( "    Find the original number\r
\n" );
document.write( "\n" );
document.write( "Given:
\n" );
document.write( "The sum of the two-digit number is 11
\n" );
document.write( "When the number is reversed, the number is 63 less than the original number\r
\n" );
document.write( "\n" );
document.write( "Representation:
\n" );
document.write( "   Let t = tens digit
\n" );
document.write( "       u = unit digit
\n" );
document.write( "      10t + u = the original two-digit number
\n" );
document.write( "      10u + t = the reversed two-digit number\r
\n" );
document.write( "\n" );
document.write( "Equation:Translate the given sentences to mathematical sentences
\n" );
document.write( "     t + u = 11 
\n" );
document.write( "     10u + t = (10t + u) - 63   Simplify
\n" );
document.write( "     9u - 9t = -63              Divide both sides by 9
\n" );
document.write( "      u - t = -7
\n" );
document.write( "  
\n" );
document.write( "Solve the two equation simultaneously by elimination or substitution.\r
\n" );
document.write( "\n" );
document.write( "  I will use elimination method
\n" );
document.write( "    t + u = 11
\n" );
document.write( "   -t + u = -7
\n" );
document.write( "  ____________
\n" );
document.write( "       2u = 4     divide 2 both sides
\n" );
document.write( "        u = 2\r
\n" );
document.write( "\n" );
document.write( "Substitute u = 2, to any of the two equations to find the other variable t.\r
\n" );
document.write( "\n" );
document.write( "   t + u = 11, u = 2
\n" );
document.write( "   t + 2 = 11
\n" );
document.write( "       t = 11 - 2
\n" );
document.write( "       t = 9\r
\n" );
document.write( "\n" );
document.write( "To find the original number, substitute t = 9 and u = 2
\n" );
document.write( "     10t + u = 10(9) + 2
\n" );
document.write( "             =  90 + 2
\n" );
document.write( "             =  92  -------------->> answer
\n" );
document.write( "     
\n" );
document.write( "  
\n" );
document.write( "If you want to check substitute t = 9 and u = 2 to any of the two equations
\n" );
document.write( "then if the two equation are true after substituting, then you're answer 
\n" );
document.write( "is correct.\r
\n" );
document.write( "\n" );
document.write( "Happy calculating\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "Rachel
\n" );
document.write( "    \n" );
document.write( "

\n" );