document.write( "Question 1164100: Cycle Center has bicycles and tricycles in the storeroom. There are at least three of each, and there are more bicycles than tricycles. There are 28 wheels altogether. How many bicycles and tricycles are in the storeroom?
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Algebra.Com's Answer #788448 by Edwin McCravy(20055) $\"\"$ $\"About$

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Cycle Center has bicycles and tricycles in the storeroom. There are at least
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document.write( "b = number of bicycles\r\n" );
document.write( "t = number of tricycles\r\n" );
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There are 28 wheels altogether.

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document.write( "2b + 3t = 28\r\n" );
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document.write( "2 is the smaller coefficient in absolute value. So write each number \r\n" );
document.write( "which is not a multiple of 2 in terms of its nearest multiple of 2.\r\n" );
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document.write( "So we only need to write the 3 as 2+1\r\n" );
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document.write( "2b + (2+1)t = 28\r\n" );
document.write( "2b + 2t + t = 28\r\n" );
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document.write( "Divide each term by 2\r\n" );
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document.write( " b + t + t/2 = 14\r\n" );
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document.write( "Isolate any fractions\r\n" );
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document.write( "         t/2 = 14 - b - t\r\n" );
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document.write( "The right side is an integer, so the left side must be equal to the\r\n" );
document.write( "same integer.  Let that integer be K\r\n" );
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document.write( "t/2 = K,    14 - b - t = K\r\n" );
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document.write( "  t = 2K,   14 - b - 2K = K\r\n" );
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document.write( "                14 - 3K = b\r\n" );
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There are more bicycles than tricycles:

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document.write( "      b > t\r\n" );
document.write( "14 - 3K > 2K\r\n" );
document.write( "     14 > 5K\r\n" );
document.write( "    2.8 > K\r\n" );
document.write( "      K ≤ 2 since K is an integer\r\n" );
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There are at least three of each

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document.write( "t = 2K ≥ 3,   b = 14 - 3K ≥ 3\r\n" );
document.write( "     K ≥ 1.5,         -3K ≥ -14\r\n" );
document.write( "     K ≥ 2              K ≤ 14/3\r\n" );
document.write( "                        K ≤ 4.333...\r\n" );
document.write( "                        K ≤ 4\r\n" );
document.write( "(since K is an integer)\r\n" );
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document.write( "Since K ≤ 2 and K ≥ 2, then K = 2\r\n" );
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document.write( "Thus t = 2K = 2(2) = 4 tricycles and\r\n" );
document.write( "     b = 14 - 3K = 14 - 3(2) = 14-6 = 8 bicycles.\r\n" );
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document.write( "Edwin

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