document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203277>Question 1203277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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? </SPAN>\n" );
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document.write( "x = cost of 1 key chain<BR>\n" );
document.write( "3x = cost of 1 pencil case<BR>\n" );
document.write( "costs are in dollars<BR>\n" );
document.write( "x > 0\r<BR>\n" );
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document.write( "3(3x) = 9x = cost of 3 pencil cases<BR>\n" );
document.write( "7x = cost of 7 key chains<BR>\n" );
document.write( "9x+7x = 16x = cost of 3 pencil cases and 7 key chains\r<BR>\n" );
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document.write( "James used 1/4 of his money to buy 3 pencil cases and 7 key chains. <BR>\n" );
document.write( "He used 1/4 of his money to spend 16x dollars.\r<BR>\n" );
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document.write( "(1/4)*(his starting amount of money) = amount spent<BR>\n" );
document.write( "(1/4)*(his starting amount of money) = 16x dollars<BR>\n" );
document.write( "his starting amount of money = 4*16x dollars<BR>\n" );
document.write( "his starting amount of money = 64x dollars\r<BR>\n" );
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document.write( "James started with 64x dollars.<BR>\n" );
document.write( "3/4 of 64x = 48x dollars left over\r<BR>\n" );
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document.write( "Or we could say: 64x - 16x = 48x\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "5/6 of 48x = 40x dollars spent on more key chains\r<BR>\n" );
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document.write( "James spent 7x dollars on 7 key chains, and then an additional 40x dollars on some more key chains. <BR>\n" );
document.write( "That's a total of 7x+40x = 47x dollars spent on all of the key chains.\r<BR>\n" );
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document.write( "Now we'll use this fact: \"He spent $30.40 more on all the key chains than on all the pencil cases.\"\r<BR>\n" );
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document.write( "Amount spent on key chains = Amount spent on pencil cases + 30.40<BR>\n" );
document.write( "47x = 9x + 30.40<BR>\n" );
document.write( "47x-9x = 30.40<BR>\n" );
document.write( "38x = 30.40<BR>\n" );
document.write( "x = 30.40/38<BR>\n" );
document.write( "x = <font color=red>0.80</font><BR>\n" );
document.write( "<font color=red>One key chain costs $0.80, aka 80 cents</font>\r<BR>\n" );
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document.write( "3x = 3*$0.80 = $2.40 is the cost of 1 pencil case.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "1 pencil case = $2.40<BR>\n" );
document.write( "3 pencil cases = 3*$2.40 = $7.20<BR>\n" );
document.write( "1 key chain = $0.80<BR>\n" );
document.write( "7 key chains = 7*$0.80 = $5.60\r<BR>\n" );
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document.write( "3 pencil cases and 7 key chains = $7.20 + $5.60 = $12.80\r<BR>\n" );
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document.write( "He spent 1/4 of his money and spent $12.80<BR>\n" );
document.write( "Therefore he started with 4*12.80 = $51.20<BR>\n" );
document.write( "3/4 of which is what he has left: (3/4)*$51.20 = $38.40<BR>\n" );
document.write( "Or we could say 51.20 - 12.80 = 38.40\r<BR>\n" );
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document.write( "After buying that first batch of pencil cases and key chains, he has $38.40 left over.<BR>\n" );
document.write( "5/6 of $38.40 = $32 is spent on additional key chains<BR>\n" );
document.write( "Each key chain is $0.80, so he must have bought 32/0.80 = 40 additional key chains.\r<BR>\n" );
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document.write( "He bought a total of 7+40 = 47 key chains<BR>\n" );
document.write( "47*0.80 = $37.60 was spent on key chains<BR>\n" );
document.write( "$7.20 was spent on pencil cases<BR>\n" );
document.write( "37.60-7.20 = 30.40 is the difference in what was spent on each item type.<BR>\n" );
document.write( "We have confirmed the answer.\r<BR>\n" );
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document.write( "Answer: One key chain costs <font color=red>$0.80</font> (aka <font color=red>80 cents</font>)<BR>\n" );
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