document.write( "Question 1033321: The sum of three numbers is 10. The sum of twice the first number, 3 times the second number, and 4 times the third number is 31. The difference between 3 times the first number and the second number is -4. Find the three numbers. \n" ); document.write( "
Algebra.Com's Answer #648003 by ankor@dixie-net.com(22740)\"\" \"About 
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Three numbers, a, b, c; write an equation for each statement
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\n" ); document.write( "Th sum of three numbers is 10
\n" ); document.write( "a + b + c = 10
\n" ); document.write( "The sum of twice the first number, 3 times the second number, and 4 times the third number is 31.
\n" ); document.write( "2a + 3b + 4c = 31
\n" ); document.write( "The difference between 3 times the first number and the second number is -4.
\n" ); document.write( "3a - b = -4
\n" ); document.write( ":
\n" ); document.write( "Multiply the 3rd equation by -1. Add all three equations. a is eliminated
\n" ); document.write( "a + b + c = 10
\n" ); document.write( "2a+ 3b+ 4c = 31
\n" ); document.write( "-3a + b + 0 = 4
\n" ); document.write( "----------------------
\n" ); document.write( "0 + 5b + 5c = 45
\n" ); document.write( "simplify, divide by 5
\n" ); document.write( "b + c = 9
\n" ); document.write( ":
\n" ); document.write( "In the 1st equation, replace a + b with 9
\n" ); document.write( "a + 9 = 10
\n" ); document.write( "a = 1
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\n" ); document.write( "Use the 3rd equation to find b, replace a with 1
\n" ); document.write( "3(1) - b = -4
\n" ); document.write( "-b = -4 - 3
\n" ); document.write( "-b = -7
\n" ); document.write( "therefore
\n" ); document.write( "b = 7
\n" ); document.write( ":
\n" ); document.write( "I'll let you find c, check your solutions in all three equations\r
\n" ); document.write( "\n" ); document.write( "Find the three numbers. \n" ); document.write( "
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