document.write( "Question 1203277: James used 1/4 of his money to buy 3 pencil cases and 7 key chains. The cost of each pencil case is 3 times the cost of each key chain. He bought some more key chains with 5/6 of his remaining money. He spent $30.40 more on all the key chains than on all the pencil cases. How much was the cost of one key chain? \n" ); document.write( "

Algebra.Com's Answer #838797 by MathTherapy(10555) $\"\"$ $\"About$

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document.write( "James used 1/4 of his money to buy 3 pencil cases and 7 key chains. The cost of each pencil case is 3 times the cost of each key chain. He bought some more key chains with 5/6 of his remaining money. He spent $30.40 more on all the key chains than on all the pencil cases. How much was the cost of one key chain?\r\n" );
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document.write( "Let original amount he had, and cost of each key chain, be A and K, respectively\r\n" );
document.write( "He used  of his money  to buy 3 pencil cases and 7 key chains, leaving  \r\n" );
document.write( "Therefore, cost of the 7 key chains (K) = 7K, and the cost of the 3 pencil cases = \r\n" );
document.write( "So, cost of 1 pencil case = \r\n" );
document.write( "Since the cost of each pencil case is 3 times the cost of each key chain, we get: \r\n" );
document.write( "                                                                                         A = 36K + 28K\r\n" );
document.write( "                                                                                         A = 64K --- eq (i)\r\n" );
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document.write( "Since he then used  of remaining money to buy more key chains, he used  to buy more key chains. \r\n" );
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document.write( "Amount spent on key chains: \r\n" );
document.write( "Amount spent on pencil cases: \r\n" );
document.write( "He spent $30.40 more on ALL key chains than on pencil cases, and so: \r\n" );
document.write( "                                                                    112K + 5A - 2A = 243.2 -- Multiplying by LCD, 8 \r\n" );
document.write( "                                                                         112K + 3A = 243.2 -- eq (ii)\r\n" );
document.write( "                                                                     112K + 3(64K) = 243.2 -- Substituting 64K for A in eq (ii)\r\n" );
document.write( "                                                                       112K + 192K = 243.2\r\n" );
document.write( "                                                                              304K = 243.2\r\n" );
document.write( "                                                     Cost of each key chain, or

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