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 #838714 by ikleyn(52834) $\"\"$ $\"About$

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\n" ); document.write( "(1) James used 1/4 of his money to buy 3 pencil cases and 7 key chains.
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\n" ); document.write( "(3) He bought some more key chains with 5/6 of his remaining money.
\n" ); document.write( "(4) He spent $30.40 more on all the key chains than on all the pencil cases.
\n" ); document.write( "How much was the cost of one key chain?
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\n" ); document.write( "\n" ); document.write( "I numbered the problem' statements for easy references.\r
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document.write( "Let x be the price of one key chain, in dollars (the unknown value under the problem's question).\r\n" );
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document.write( "Then the price for one pencil case is 3x dollars, according to the problem's statement (2).\r\n" );
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document.write( "The cost of the first purchase (3 pencil cases and 7 key chains) was  3(3x) + 7x = 9x + 7x = 16x.\r\n" );
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document.write( "This cost was 1/4 of his money originally - hence, the original amount of money was  4*(16x) = 64x.\r\n" );
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document.write( "    After his first purchase, the remaining money was  = 48x.\r\n" );
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document.write( "    James bought additional key chains for  = 40x dollars.\r\n" );
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document.write( "For key chains, he spent, in all,  7x + 40 = 47x  dollars.\r\n" );
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document.write( "For all pencil cases, he spent 3*(3x) = 9x dollars.\r\n" );
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document.write( "The difference is  47x - 9x = 38x.\r\n" );
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document.write( "From (4), we have this equation for the difference\r\n" );
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document.write( "    38x = 30.40 dollars.\r\n" );
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document.write( "Hence,  x =  = 0.80 dollars.\r\n" );
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document.write( "ANSWER.  The cost of one key chain is $0.80.\r\n" );
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