document.write( "Question 603431: i have 100 dollars and need to buy a hundred items and one item cost 3 dollars the other cost .50 cents and the last one cost 10 dollars how many of each will i have
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Algebra.Com's Answer #380702 by AnlytcPhil(1806) $\"\"$ $\"About$

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i have 100 dollars and need to buy a hundred items and one item cost 3 dollars the other cost .50 cents and the last one cost 10 dollars how many of each will i have
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document.write( "Let x = number of $3 items\r\n" );
document.write( "Let y = number of $.50 items\r\n" );
document.write( "Let z = number of $10 items\r\n" );
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document.write( " x +    y +   z = 100    <--item equation\r\n" );
document.write( "3x +  .5y + 10z = 100    <--money equation\r\n" );
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document.write( "Clear the decimal of the second equation by multiplying it through by 2\r\n" );
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document.write( " x +  y +   z = 100\r\n" );
document.write( "6x +  y + 20z = 100\r\n" );
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document.write( "Subtracting the first equation from the second gives\r\n" );
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document.write( "5x      + 19z = 100\r\n" );
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document.write( "Solve for x:\r\n" );
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document.write( "          5x = 100 - 19z\r\n" );
document.write( "           x =  20 - \r\n" );
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document.write( "z has to be a multiple of 5 for  to be a whole number\r\n" );
document.write( "and if z were bigger than 5, x would be negative, so the only value\r\n" );
document.write( "z can take on is 5 which makes x = 20 - 19 = 1, so  substituting in\r\n" );
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document.write( "x + y + z = 100\r\n" );
document.write( "1 + y + 5 = 100\r\n" );
document.write( "    y + 6 = 100\r\n" );
document.write( "        y = 94\r\n" );
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document.write( "1 of the first item, 94 of the second item and 5 of the 3rd.\r\n" );
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document.write( "Edwin

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