document.write( "Question 1205779: There were 5c 10c and 20c coins in Joel's wallet in the ratio of 2:6:7 respectively. If he takes out half the number of 5c and half the number of 10c coins they would make up $4.20
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Algebra.Com's Answer #842818 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "We use the fact that if 3 quantities are in the ratio \r\n" );
document.write( "of a:b:c, then the fraction of the total which the first,\r\n" );
document.write( "second and third quantities are, are respectively,\r\n" );
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document.write( "There were 5c 10c and 20c coins in Joel's wallet in the ratio\r\n" );
document.write( "of 2:6:7 respectively. If he takes out half the number of 5c \r\n" );
document.write( "and half the number of10c coins they would make up $4.20. \r\n" );
document.write( "How many 20c coins in his wallet?let x = number of 5c coins.\r\n" );
document.write( "let y = number of 10c coins.\r\n" );
document.write( "let z = number of 20c coins.\r\n" );
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document.write( "The fraction of 5c coins is .\r\n" );
document.write( "The fraction of 10c coins is .\r\n" );
document.write( "the fraction of 20c coins is .\r\n" );
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document.write( "Since he had x 5c coins, then the value of them would be 5x cents.\r\n" );
document.write( "When he takes out half of them, only 2.5x cents.\r\n" );
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document.write( "Suppose he had y 10c coins, then the value of them would be 10y cents.\r\n" );
document.write( "When he takes out half of them, that's only 5y cents.\r\n" );
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document.write( "2.5x + 5y = 420\r\n" );
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document.write( "Multiply through by 2\r\n" );
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document.write( "5x + 10y = 840\r\n" );
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document.write( "Divide through by 5\r\n" );
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document.write( "x + 2y = 168\r\n" );
document.write( "x = 168 - 2y\r\n" );
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document.write( "Substitute for x\r\n" );
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document.write( "Divide the first through by 2 and the second through by 3\r\n" );
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document.write( "Solve the first for z\r\n" );
document.write( "z = 1092-14y\r\n" );
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document.write( "Substitute in the second equation\r\n" );
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document.write( "-336+7y-2(1092-14y) = 0\r\n" );
document.write( "-336+7y-2184+28y = 0\r\n" );
document.write( "35y-2520 = 0\r\n" );
document.write( "35y = 2520\r\n" );
document.write( "y = 72\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "z = 1092-14y\r\n" );
document.write( "z = 1092-1008\r\n" );
document.write( "z = 84\r\n" );
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document.write( "x = 168 - 2y\r\n" );
document.write( "x = 168 - 2(72)\r\n" );
document.write( "x = 168 - 144\r\n" );
document.write( "x = 24\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "So there are 24 5c coins, 72 10c coins, 84 20c coins\r\n" );
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document.write( "Edwin \n" );
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