document.write( "Question 777636: In a group of men, women, boys, and girls, there were 10 more men than boys and 5 more women than girls. If there are twice as many boys as girls and 105 people in all, how many are men? \n" ); document.write( "
Algebra.Com's Answer #474217 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
In a group of men, women, boys, and girls, there were 10 more men than boys
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document.write( "M = B+10\r\n" );
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\n" ); document.write( "and 5 more women than girls.
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document.write( "W = G+5\r\n" );
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\n" ); document.write( "If there are twice as many boys as girls
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document.write( "B = 2G\r\n" );
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\n" ); document.write( "and 105 people in all,
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document.write( "M+W+B+G = 105\r\n" );
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document.write( "(1)   M = B+10\r\n" );
document.write( "(2)   W = G+5\r\n" );
document.write( "(3)   B = 2G\r\n" );
document.write( "(4)   M+W+B+G = 105\r\n" );
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document.write( "Using (3) substitute 2G for B in (1) and (4)\r\n" );
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document.write( "(5)   M = 2G+10\r\n" );
document.write( "      M+W+2G+G = 105\r\n" );
document.write( "(6)   M+W+3G = 105\r\n" );
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document.write( "So now our system is\r\n" );
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document.write( "(5)   M = 2G+10\r\n" );
document.write( "(2)   W = G+5\r\n" );
document.write( "(6)   M+W+3G = 105\r\n" );
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document.write( "Using (2) substitute G+5 for W in (6)\r\n" );
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document.write( "(6)   M+W+3G = 105\r\n" );
document.write( "      M+G+5+3G = 105\r\n" );
document.write( "(7)   M+4G = 100\r\n" );
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document.write( "Using (5), substitute 2G+10 for M in (7):\r\n" );
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document.write( "(7)   M+4G = 100\r\n" );
document.write( "      2G+10+4G = 100\r\n" );
document.write( "      6G = 90\r\n" );
document.write( "(8)    G = 15\r\n" );
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document.write( "Using (8), substitute 15 for G in (7)\r\n" );
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document.write( "(7)   M+4G = 100\r\n" );
document.write( "      M+4(15) = 100\r\n" );
document.write( "      M+60 = 100\r\n" );
document.write( "(9)      M = 40\r\n" );
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\n" ); document.write( "how many are men?
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document.write( "That's the answer.  But to check we need W and B\r\n" );
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document.write( "Using (8), substitute 15 for G in (2)\r\n" );
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document.write( "(2)   W = G+5\r\n" );
document.write( "      W = 15+5\r\n" );
document.write( "      W = 20\r\n" );
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document.write( "Using (8), substitute 15 for G in (3)\r\n" );
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document.write( "(3)   B = 2G\r\n" );
document.write( "      B = 2(15)\r\n" );
document.write( "      B = 30\r\n" );
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document.write( "Answer: 40 men, 20 women, 30 boys, and 15 girls.\r\n" );
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document.write( "Checking:\r\n" );
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\n" ); document.write( "In a group of men, women, boys, and girls, there were 10 more men than boys
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document.write( "That checks, because 40 is 10 more than 30\r\n" );
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\n" ); document.write( "and 5 more women than girls.
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document.write( "That checks, because 20 is 5 more than 15\r\n" );
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\n" ); document.write( "If there are twice as many boys as girls
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document.write( "That checks, because 30 is twice as many as 15\r\n" );
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\n" ); document.write( "and 105 people in all,
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document.write( "That checks because 40+20+30+15 = 105\r\n" );
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document.write( "Edwin
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