document.write( "Question 779727: I have $5.50 total in my pocket, consisting of nickels, dimes and quarters. There are 30 coins total. There are also, 2 times as many dimes as nickels. How many of each coin do I have in my pocket?
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Algebra.Com's Answer #475344 by Edwin McCravy(20056) $\"\"$ $\"About$

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I have $5.50 total in my pocket, consisting of nickels, dimes and quarters. There are 30 coins total. There are also, 2 times as many dimes as nickels. How many of each coin do I have in my pocket?\r
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\n" ); document.write( "\n" ); document.write( ">>There are 30 coins total.<<
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document.write( "     n + d + q = 30\r\n" );
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\n" ); document.write( ">>I have $5.50 total...<<
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document.write( "$0.05n + $0.10d + $0.25q = $5.50\r\n" );
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document.write( "    5n +    10d +    25q = 550\r\n" );
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\n" ); document.write( ">>...2 times as many dimes as nickels...<<
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document.write( "    d = 2n\r\n" );
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document.write( " n +   d +   q =  30\r\n" );
document.write( "5n + 10d + 25q = 550\r\n" );
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document.write( "Substitute 2n for d in both of those:\r\n" );
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document.write( " n +    2n  +   q =  30\r\n" );
document.write( "           3n + q = 30\r\n" );
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document.write( "5n + 10(2n) + 25q = 550\r\n" );
document.write( "   5n + 20n + 25q = 550\r\n" );
document.write( "        25n + 25q = 550\r\n" );
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document.write( "Divide through by 25\r\n" );
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document.write( "            n + q = 22\r\n" );
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document.write( "Solve for q:\r\n" );
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document.write( "                q = 22 - n\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "           3n + q = 30\r\n" );
document.write( "    3n + (22 - n) = 30\r\n" );
document.write( "      3n + 22 - n = 30\r\n" );
document.write( "          2n + 22 = 30\r\n" );
document.write( "               2n = 8\r\n" );
document.write( "                n = 4\r\n" );
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document.write( "Substitute in\r\n" );
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document.write( "                q = 22 - n   \r\n" );
document.write( "                q = 22 - 4\r\n" );
document.write( "                q = 18\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "                    d = 2n\r\n" );
document.write( "                    d = 2(4)\r\n" );
document.write( "                    d = 8\r\n" );
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document.write( "Answer:\r\n" );
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document.write( "18 quarters = 18×$0.25 = $4.50\r\n" );
document.write( " 8 dimes    =  8×$0.10 =  0.80\r\n" );
document.write( " 4 nickels  =  4×$0.05 =  0.20          \r\n" );
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document.write( "30 coins         value = %5.50\r\n" );
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document.write( "Edwin

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