document.write( "Question 1124074: The sum of three numbers is 10. The sum of twice the first​ number, 5 times the second​ number, and 6 times the third number is 53. The difference between 7 times the first number and the second number is 4. \r
\n" ); document.write( "\n" ); document.write( "Find the three numbers.
\n" ); document.write( "first​ number:\r
\n" ); document.write( "\n" ); document.write( "second​ number: \r
\n" ); document.write( "\n" ); document.write( "third​ number: \n" ); document.write( "
Algebra.Com's Answer #854135 by MathTherapy(10791)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The sum of three numbers is 10.  The sum of twice the first​ number, 5 times the second​ number, and 6 times\r\n" );
document.write( "the third number is 53.  The difference between 7 times the first number and the second number is 4.  \r\n" );
document.write( "\r\n" );
document.write( "Find the three numbers.\r\n" );
document.write( "first​ number:\r\n" );
document.write( "second​ number: \r\n" );
document.write( "third​ number:\r\n" );
document.write( "********************\r\n" );
document.write( "This is MUCH simpler than the other person made it out to be.\r\n" );
document.write( "\r\n" );
document.write( "Let the 1st number be F, and the 2nd, S\r\n" );
document.write( "Since the sum of the 3 numbers is 10, the 3rd is: 10 - F - S\r\n" );
document.write( "\r\n" );
document.write( "The sum of twice the first, 5 times the second, and 6 times the third is 53, gives us:\r\n" );
document.write( "                          2F + 5S + 6(10 - F - S) = 53\r\n" );
document.write( "                           2F + 5S + 60 - 6F - 6S = 53\r\n" );
document.write( "                                                     - 4F - S = - 7 ---- eq (i)\r\n" );
document.write( "\r\n" );
document.write( "The difference between 7 times the first and the second number is 4, gives us: \r\n" );
document.write( "                                                       7F - S = 4 ---- eq (ii)  \r\n" );
document.write( "\r\n" );
document.write( "                                                    - 4F - S = - 7 --- eq (i)\r\n" );
document.write( "                                                      7F - S =   4 ---- eq (ii) \r\n" );
document.write( "                                                         11F = 11 ---- Subtracting eq (i) from eq (ii)\r\n" );
document.write( "                                First number, or \"F+=+11%2F11+=+highlight%281%29\"\r\n" );
document.write( "\r\n" );
document.write( "                                                  7(1) - S = 4 ---- Substituting 1 for F in eq (ii)\r\n" );
document.write( "                                                       7 - S = 4\r\n" );
document.write( "                                                          - S = 4 - 7\r\n" );
document.write( "                                                          - S = - 3\r\n" );
document.write( "                          Second number, or \"S+=+%28-+3%29%2F%28-+1%29+=+highlight%283%29\"\r\n" );
document.write( "\r\n" );
document.write( "Third number: 10 - F - S = 10 - 1 - 3 = 10 - 4 = 6
\n" ); document.write( "
\n" );