document.write( "Question 345372: Eddie spills his cash register drawer on the floor and has to sweep up the coins. He has 680 coins, which are a mixture of pennies, nickels, dimes, and quarters. There are 10 times as many pennies as dimes, and half as many quarters as dimes. If he has $25.00, how many dimes are there? \n" ); document.write( "
Algebra.Com's Answer #246997 by Edwin McCravy(20077)\"\" \"About 
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Eddie spills his cash register drawer on the floor and has to sweep up the coins. He has 680 coins, which are a mixture of pennies, nickels, dimes, and quarters. There are 10 times as many pennies as dimes, and half as many quarters as dimes. If he has $25.00, how many dimes are there?\r
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\n" ); document.write( "\n" ); document.write( ">>...He has 680 coins, which are a mixture of pennies, nickels, dimes,
\n" ); document.write( "and quarters...<<\r
\n" ); document.write( "\n" ); document.write( "\"P+%2B+N+%2B+D+%2B+Q+=+680\" \r
\n" ); document.write( "\n" ); document.write( ">>...There are 10 times as many pennies as dimes,...<<\r
\n" ); document.write( "\n" ); document.write( "\"P+=+10D\"\r
\n" ); document.write( "\n" ); document.write( ">>...half as many quarters as dimes...<<\r
\n" ); document.write( "\n" ); document.write( "\"Q+=+expr%281%2F2%29D\"\r
\n" ); document.write( "\n" ); document.write( ">>...he has $25.00...<<
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document.write( "\"P+%2B+5N+%2B+10D+%2B+25Q+=+2500\"\r\n" );
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document.write( "   \r\n" );
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document.write( "Substitute 10D for P, and \"expr%281%2F2%29D\" for Q in the first \r\n" );
document.write( "equation:\r\n" );
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document.write( "\"P+%2B+5N+%2B+10D+%2B+25Q+=+2500\"\r\n" );
document.write( "\"10D+%2B+5N+%2B+10D+%2B+25%28expr%281%2F2%29D%29+=+2500\"\r\n" );
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document.write( "\"10D+%2B+5N+%2B+10D+%2B+expr%2825%2F2%29D+=+2500\"\r\n" );
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document.write( "Clear of fractions by multiplying through by 2\r\n" );
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document.write( "\"20D+%2B+10N+%2B+20D+%2B+25D+=+5000\"\r\n" );
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document.write( "\"65D+%2B+10N+=+5000\"\r\n" );
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document.write( "Divide through by 5\r\n" );
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document.write( "\"13D+%2B+2N+=+1000\"\r\n" );
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document.write( "-----\r\n" );
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document.write( "Substitute 10D for P, and \"expr%281%2F2%29D\" for Q in the fourth\r\n" );
document.write( "equation:\r\n" );
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document.write( "\"P+%2B+N+%2B+D+%2B+Q+=+680\"\r\n" );
document.write( "\"10D+%2B+N+%2B+D+%2B+expr%281%2F2%29D+=+680\"\r\n" );
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document.write( "\"11D+%2B+N+%2B+expr%281%2F2%29D+=+680\"\r\n" );
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document.write( "Clear of fractions by multiplying through by 2\r\n" );
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document.write( "\"22D+%2B+2N+%2B+D+=+1360\"\r\n" );
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document.write( "\"23D+%2B+2N+=+1360\"\r\n" );
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document.write( "Now we have this system of two equations in 2 unknowns:\r\n" );
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document.write( "\"system%2813D+%2B+2N+=+1000%2C23D+%2B+2N+=+1360%29\"\r\n" );
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document.write( "Solve that and get 36 dimes and 266 nickels.\r\n" );
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document.write( "So the answer is 36 for the number of dimes.\r\n" );
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document.write( "However in order to check the problem, we need to find \r\n" );
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document.write( "the number of pennies and quarters.\r\n" );
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document.write( "\"P+=+10D\"\r\n" );
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document.write( "\"P+=+10%2836%29\"\r\n" );
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document.write( "\"P+=+360\"\r\n" );
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document.write( "\"Q+=+expr%281%2F2%29D\"\r\n" );
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document.write( "\"Q+=+expr%281%2F2%29%2836%29\"\r\n" );
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document.write( "\"Q+=+18\"\r\n" );
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document.write( "360 pennies, 266 nickels, 36 dimes, 18 quarters\r\n" );
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document.write( "Checking:\r\n" );
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\n" ); document.write( ">>...He has 680 coins,...<<
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document.write( "Checking: 360+266+36+18 = 680\r\n" );
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document.write( "That checks.\r\n" );
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\n" ); document.write( ">>...There are 10 times as many pennies as dimes,...<<
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\r\n" );
document.write( "Checking 360 is 10 times 36\r\n" );
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document.write( "That checks. \r\n" );
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\n" ); document.write( ">>...half as many quarters as dimes...<<
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document.write( "Checking: 18 is half of 36.\r\n" );
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document.write( "That checks\r\n" );
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\n" ); document.write( ">>...he has $25.00...<<
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\r\n" );
document.write( "360 pennies = 360($.10) = $ 3.60\r\n" );
document.write( "266 nickels = 266($.05) = $13.30\r\n" );
document.write( "36 dimes = 36($.10)     = $ 3.60 \r\n" );
document.write( "18 quarters = 18($.25)  = $ 4.50\r\n" );
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document.write( "                  Total = $25.00\r\n" );
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document.write( "That checks.\r\n" );
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document.write( "Answer: 36 dimes.\r\n" );
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document.write( "Edwin
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