document.write( "Question 647353: A bag contain 3 types of coins namely $1, $2, $5. There are 30 coins
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Algebra.Com's Answer #406146 by Edwin McCravy(20086) $\"\"$ $\"About$

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A bag contain 3 types of coins namely $1, $2, $5. There are 30 coins
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document.write( "Let x = the number of $1 coins\r\n" );
document.write( "Let y = the number of $2 coins\r\n" );
document.write( "Let z = the number of $5 coins\r\n" );
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document.write( " x +  y +  z =  30     <-- 30 coins\r\n" );
document.write( "1x + 2y + 5z = 100     <-- $100 total\r\n" );
document.write( "           y = 2x      <-- twice as many $2 coins as $1 coins\r\n" );
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document.write( "Rearrange the 3rd equation, so that like letters line up in the\r\n" );
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document.write( "  x +  y +  z =  30   \r\n" );
document.write( "  x + 2y + 5z = 100     \r\n" );
document.write( "-2x +  y      =   0\r\n" );
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document.write( "To solve using Cramer's rule:\r\n" );
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document.write( "Write in all the 1 coefficients and 0 for\r\n" );
document.write( "the coefficient of the missing variable z in the\r\n" );
document.write( "third equation:\r\n" );
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document.write( "Cramer's rule:\r\n" );
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document.write( "There are 4 columns,\r\n" );
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document.write( "1. The column of x-coefficients \r\n" );
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document.write( "2. The column of y-coefficients \r\n" );
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document.write( "3. The column of z-coefficients  \r\n" );
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document.write( "4. The column of constants:     \r\n" );
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document.write( "There are four determinants:\r\n" );
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document.write( "1. The determinant  consists of just the three columns\r\n" );
document.write( "of x, y, and z coefficients. in that order, but does not\r\n" );
document.write( "contain the column of constants.\r\n" );
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document.write( ". \r\n" );
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document.write( "It has value .  I'm assuming you know how to find the\r\n" );
document.write( "value of a 3x3 determinant, for that's a subject all by itself.\r\n" );
document.write( "If you don't know how, post again asking how. \r\n" );
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document.write( "2. The determinant  is like the determinant \r\n" );
document.write( "except that the column of x-coefficients is replaced by the\r\n" );
document.write( "column of constants.   does not contain the column \r\n" );
document.write( "of x-coefficients.\r\n" );
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document.write( "It has value .\r\n" );
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document.write( "3. The determinant  is like the determinant \r\n" );
document.write( "except that the column of y-coefficients is replaced by the\r\n" );
document.write( "column of constants.   does not contain the column \r\n" );
document.write( "of y-coefficients.\r\n" );
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document.write( ".\r\n" );
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document.write( "It has value .\r\n" );
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document.write( "4. The determinant  is like the determinant \r\n" );
document.write( "except that the column of z-coefficients is replaced by the\r\n" );
document.write( "column of constants.   does not contain the column \r\n" );
document.write( "of z-coefficients.\r\n" );
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document.write( ".\r\n" );
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document.write( "It has value .\r\n" );
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document.write( "Now the formulas for x, y and z are\r\n" );
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document.write( "Answer: 5 $1 coins, 10 $2 coins, 15, $5 coins`\r\n" );
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document.write( "Edwin

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