document.write( "Question 1176096: Hi
\n" ); document.write( "Bob had some money left after spending $9 on 4 files and 6 pens. If he were to buy one more file, he would be short 30cents. If he were to buy one more pen he would have 70 cents left.
\n" ); document.write( "What was the cost of each file.
\n" ); document.write( "How much money did he have at first. \r
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Algebra.Com's Answer #802127 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " This problem is tricky: I made several attempts before I came to right setup.\r
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document.write( "Let F be the price for each file;  P be the price for each pen, and\r\n" );
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document.write( "let X be the amount of money that Bob had initially.\r\n" );
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document.write( "Then, based on the problem's description, we can write these THREE equations for three unknowns\r\n" );
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document.write( "    4F + 6P = 900     cents     (1)     (he spent $9 on 4F and 6P)\r\n" );
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document.write( "    5F + 6P = X + 30  cents     (2)     (he would be short 30 cents)\r\n" );
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document.write( "    4F + 7P = X - 70  cents     (3)     (he would be 70 cents left)\r\n" );
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document.write( "        The setup is just completed. \r\n" );
document.write( "        As I said at the beginning, it is tricky.\r\n" );
document.write( "        But the solution of equations is simple.\r\n" );
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document.write( "To solve them, first subtract equation (3) from equation ((2).  You will get\r\n" );
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document.write( "    F - P   =     100  cents.   (4)\r\n" );
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document.write( "Next, express  F = P + 100 from (4), and substitute it into equation (1).  You will get\r\n" );
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document.write( "    4(P + 100) + 6P = 900\r\n" );
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document.write( "        10P         = 900 - 400 = 500\r\n" );
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document.write( "          P                     = 500/10 = 50.\r\n" );
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document.write( "Next, from equation (1),  4F + 6*50 = 900,  4F = 900 - 300 = 600,  F = 600/4 = 150.\r\n" );
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document.write( "Thus, the price for one file is $1.50;  the price for one pen is  P = F - 100 = 150-100 = 50 = $0.5  (from equation (4))\r\n" );
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document.write( "and  X = 5F + 6P - 30 = 5*150 + 6*50 - 30 = 1020 cents = $10.20.  (from equation (2) )\r\n" );
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document.write( "ANSWER.  The price for each file is  $1.50.  Bob had  $10.20  originally.\r\n" );
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