document.write( "Question 1144730: The sum of 3 numbers is 30. The sum of the first and second is twice the third. The sun of the second and third is 3 more than twice the first. What is the third number? \n" ); document.write( "
Algebra.Com's Answer #765919 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "From the first two sentences\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"The sum of 3 numbers is 30. The sum of the first and second is twice the third.\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "it is CLEAR that  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    (First + Second + Third) = (First+Second) + Third = 2*Third + Third = 3*Third = 30,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which implies  that Third = 10.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the \"Third\" number is found MENTALLY and MOMENTARILY without using equations.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "But it is NOT ENOUGH to complete the solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The complete solution must assure that the second and the third numbers EXIST and that the problem is not SELF-CONTRADICTORY.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For it, the second and the third numbers should be found.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "By knowing the THIRD, it is just problem for 2 equations in 2 unknowns.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The solution DOES EXIST, indeed, and it is  FIRST = 9  and SECOND = 11.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At this point, the solution is, finally, completed.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );