document.write( "Question 229377: The sum of three numbers is 16. The sum of twice the first number, 3 times the second number, and 4 times the third number is 46. The difference between 5 times the first number and the second number is 31. Find the three numbers. \n" ); document.write( "
Algebra.Com's Answer #170079 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Three numbers, x, y, z
\n" ); document.write( ";
\n" ); document.write( "Write an equation for each statement:
\n" ); document.write( ":
\n" ); document.write( "\"The sum of three numbers is 16.\"
\n" ); document.write( "x + y + z = 16
\n" ); document.write( ":
\n" ); document.write( "\" The sum of twice the first number, 3 times the second number, and 4 times the third number is 46.\"
\n" ); document.write( "2x = 3y + 4z = 46
\n" ); document.write( ":
\n" ); document.write( "\" The difference between 5 times the first number and the second number is 31.\"
\n" ); document.write( "5x - y = 31
\n" ); document.write( "-y = 31 - 5x
\n" ); document.write( "y = 5x - 31; multiplied by -1
\n" ); document.write( ":
\n" ); document.write( " Find the three numbers.
\n" ); document.write( ":
\n" ); document.write( "Replace y with (5x-31) in the 1st and 2nd equation
\n" ); document.write( "x + (5x-31) + z = 16
\n" ); document.write( "6x + z = 16 + 31
\n" ); document.write( "6x + z = 47
\n" ); document.write( ":
\n" ); document.write( "2x = 3(5x-31) + 4z = 46
\n" ); document.write( "2x = 15x - 93 + 4z = 46
\n" ); document.write( "17x + 4z = 46 + 93
\n" ); document.write( "17x + 4z = 139
\n" ); document.write( ";
\n" ); document.write( "Multiply the 1st 2 unknown equation by 4, subtract the 2nd
\n" ); document.write( "24x + 4z = 188
\n" ); document.write( "17x + 4z = 139
\n" ); document.write( "----------------subtraction eliminates z
\n" ); document.write( "7x = 49
\n" ); document.write( "x = \"49%2F7\"
\n" ); document.write( "x = 7
\n" ); document.write( ":
\n" ); document.write( "Find z using 6x + z = 47
\n" ); document.write( "6(7) + z = 47
\n" ); document.write( "42 + z = 47
\n" ); document.write( "z = 47 - 42
\n" ); document.write( "z = 5
\n" ); document.write( ";
\n" ); document.write( "Use y = 5x - 31 to find y
\n" ); document.write( "y = 5(7) - 31
\n" ); document.write( "y = 35 - 31
\n" ); document.write( "y = 4
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check our solution in the statement:
\n" ); document.write( "\"The sum of twice the first number, 3 times the second number, and 4 times the third number is 46.\"
\n" ); document.write( "2(7) + 3(4) + 4(5) =
\n" ); document.write( "14 + 12 + 20 = 46 \n" ); document.write( "
\n" );