document.write( "Question 1105587: A, B, C, and D, are distinct digits, and 4(AAB) = CDA. If C is less than d, find the sum of a +b+c+d \n" ); document.write( "

Algebra.Com's Answer #720452 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A, B, C, and D, are distinct digits, and 4(AAB) = CDA. If C is less than d, find the sum of a +b+c+d
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "1.  From 4*(AAB) = CDA,  it follows that  A is an even number/digit different from zero and not more than 2.\r\n" );
document.write( "\r\n" );
document.write( "    It leaves only one possibility for A:  A = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  Since A = 2, it leaves only two possibilities for C:  C= 8  or  C= 9.\r\n" );
document.write( "\r\n" );
document.write( "    Since, in addition,  C is less than D,  it implies that C= 8  and  D= 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  Then CDA = 892,  and it implies that  AAB =  = 223.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "4.  Thus we just found that  AAB = 223,  CDA = 892,\r\n" );
document.write( "\r\n" );
document.write( "    A= 2,  B= 3,  C= 8,  D= 9.\r\n" );
document.write( "\r\n" );
document.write( "    Then A + B + C + D = 2 + 3 + 8 + 9 = 22.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  A + B + C + D = 22.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );