document.write( "Question 1192437: To be exact, this word problem is all about Systems of Linear Equation in Three Variables.\r
\n" ); document.write( "\n" ); document.write( "There are three boys, Cyril, Ryan, and Guye. The sum of their ages is twenty years. Cyril’s age added to Guye’s is four-time Ryan’s age, and Ryan’s age added to Cyril’s is four times Guye’s. How old are three boys?\r
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Algebra.Com's Answer #824309 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Ikelyn thinks you've already finished the section on 3 equations in 3 unknowns,\r\n" );
document.write( "and that now you are studying clever ways of getting answers without using the\r\n" );
document.write( "methods of solving 3 equations in 3 unknowns. Or --\r\n" );
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document.write( "She might be trying to show us how smart she is (or how dumb I am for not using\r\n" );
document.write( "her \"clever\" method).\r\n" );
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document.write( "Anyway,\r\n" );
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document.write( "Instead of doing your homework for you, I'll do one exactly like yours\r\n" );
document.write( "but change all the numbers:  I'll do this one:\r\n" );
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\n" ); document.write( "There are three boys, Cyril, Ryan, and Guye. The sum of their ages
\n" ); document.write( "is sixty years. Cyril’s age added to Guye’s is five times Ryan’s age,
\n" ); document.write( "and Ryan’s age added to Cyril’s is five times Guye’s. How old are
\n" ); document.write( "the three boys?

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document.write( "The sum of their ages is sixty years.
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document.write( "C + R + G = 60

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document.write( "Cyril’s age added to Guye’s is five times Ryan’s age,
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document.write( "G+C = 5R

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document.write( "and Ryan’s age added to Cyril’s is five times Guye’s.
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document.write( "C + R = 5G\r\n" );
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document.write( "\"system%28C%2BR%2BG=60%2C+G%2BC=5R%2C+C%2BR=5G%29\"\r\n" );
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document.write( "Get the terms in order and lined up vertically\r\n" );
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document.write( "  \r\n" );
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document.write( "Eliminate C and G by multiplying the first equation by -1\r\n" );
document.write( "and adding the second equation to it:\r\n" );
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document.write( "-C -  R - G = -60\r\n" );
document.write( " C - 5R + G =   0\r\n" );
document.write( "-----------------\r\n" );
document.write( " 0  -6R + 0 = -60\r\n" );
document.write( "        -6R = -60\r\n" );
document.write( "          R = 10\r\n" );
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document.write( "Substitute 10 for R in all three equations:\r\n" );
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document.write( "Simplify\r\n" );
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document.write( "   \r\n" );
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document.write( "Simplify further:\r\n" );
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document.write( "The first two equations are the same so eliminate one of them:\r\n" );
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document.write( "Solve the first equation for C\r\n" );
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document.write( "C = 50 - G\r\n" );
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document.write( "Substitute (50 - G) for C in the second equation:\r\n" );
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document.write( "50 - G - 5G = -10\r\n" );
document.write( "    50 - 6G = -10\r\n" );
document.write( "        -6G = -60\r\n" );
document.write( "          G = 10\r\n" );
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document.write( "Substitute 10 for R and 10 for G in \r\n" );
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document.write( "C + R + G = 60 \r\n" );
document.write( "C + 10 + 10 = 60\r\n" );
document.write( "     C + 20 = 60\r\n" );
document.write( "          C = 40  <--Cyril is a 40-year-old \"BOY\". lol\r\n" );
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document.write( "Now do yours the same way. Cyril will be a BOY in your problem. lol\r\n" );
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document.write( "Edwin
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