document.write( "Question 259667: Anna bought 12 pieces of gum consisting of only red gumballs and white gumballs. The total cost is $1.29. The red gumballs each cost 3 cents more than each white gumball, and she bought fewer reds than whites. How many white gumballs did she buy? How many red? \n" ); document.write( "

Algebra.Com's Answer #191228 by Edwin McCravy(20060) $\"\"$ $\"About$

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Anna bought 12 pieces of gum consisting of only red gumballs and white gumballs. The total cost is $1.29. The red gumballs each cost 3 cents more than each white gumball, and she bought fewer reds than whites. How many white gumballs did she buy? How many red?
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document.write( "Ler R = thr number of red ones.\r\n" );
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document.write( "Let W = the number of white ones.\r\n" );
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document.write( "Let x = the price of each white ones.\r\n" );
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document.write( "Then x+3 = the price of each red one\r\n" );
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document.write( "So we have the system:\r\n" );
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document.write( "R(x+3) + Wx = 129\r\n" );
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document.write( "Rx + 3R + Wx = 129\r\n" );
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document.write( "Rx + Wx = 129-3R\r\n" );
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document.write( "x(R + W) = 129-3R\r\n" );
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document.write( "and since R + W = 12,\r\n" );
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document.write( "x(12) = 129-3R\r\n" );
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document.write( "12x + 3R = 129\r\n" );
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document.write( "4x + R = 43\r\n" );
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document.write( "R = 43-4x\r\n" );
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document.write( "-----------\r\n" );
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document.write( "R + W = 12, so\r\n" );
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document.write( "W = 12 - R\r\n" );
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document.write( "W = 12 - (43-4x)\r\n" );
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document.write( "W = 12-43+4x\r\n" );
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document.write( "W = 4x-31\r\n" );
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document.write( "----------------\r\n" );
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document.write( "    R < W, so   \r\n" );
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document.write( "43-4x < 4x-31\r\n" );
document.write( "  -8x < -74 \r\n" );
document.write( "    x > 9.25\r\n" );
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document.write( "Since R > 0,\r\n" );
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document.write( "43-4x > 0\r\n" );
document.write( "  -4x > -43\r\n" );
document.write( "    x < 10.75\r\n" );
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document.write( "So 9.25 < x < 10.75\r\n" );
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document.write( "The only whole number of cents possible between those\r\n" );
document.write( "two values is 10 cents.\r\n" );
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document.write( "R = 43-4x = 43-4(10) = 43-40 = 3\r\n" );
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document.write( "W = 12 - R = 12 - 3 = 9\r\n" );
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document.write( "So there is one solution:\r\n" );
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document.write( "3 Reds, 9 Whites, Reds cost 10 cents each, Whites cost 13 cents each\r\n" );
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document.write( "Edwin

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