document.write( "Question 1059633: I can only use 18 coins to creat the amount 2.50 using only quarters nickels and dimes how many quarters nickels and dimes are used \n" ); document.write( "
Algebra.Com's Answer #674683 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "25q + 10d + 5n = 250\r\n" );
document.write( "  q +   d +  n =  18\r\n" );
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document.write( "Let's eliminate d by multiplying the \r\n" );
document.write( "second equation through by -10 and\r\n" );
document.write( "adding the two equations:\r\n" );
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document.write( " 25q + 10d +  5n = 250\r\n" );
document.write( "-10q - 10d - 10n = 180\r\n" );
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document.write( " 15q       -  5n =  70\r\n" );
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document.write( "Divide through by 5\r\n" );
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document.write( "  3q - n = 14\r\n" );
document.write( " 3q - 14 = n \r\n" );
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document.write( "So the smallest possible number of quarters is 5 \r\n" );
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document.write( "Substitute q = 5 \r\n" );
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document.write( "n = 3q - 14 = 3(5) - 14 = 15 - 14 = 1  \r\n" );
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document.write( "Substitute q = 5 and n = 1 in   \r\n" );
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document.write( "q + d + n = 18\r\n" );
document.write( "5 + d + 1 = 18\r\n" );
document.write( "    d + 6 = 18\r\n" );
document.write( "        d = 12\r\n" );
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document.write( "So 1 solution is 5 quarters, 1 nickel and 12 dimes\r\n" );
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document.write( "Substitute q = 6 \r\n" );
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document.write( "n = 3q - 14 = 3(6) - 14 = 18 - 14 = 4  \r\n" );
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document.write( "Substitute q = 6 and n = 4 in   \r\n" );
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document.write( "q + d + n = 18\r\n" );
document.write( "6 + d + 4 = 18\r\n" );
document.write( "   d + 10 = 18\r\n" );
document.write( "        d = 8\r\n" );
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document.write( "So 1 solution is 6 quarters, 4 nickels and 8 dimes\r\n" );
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document.write( "Substitute q = 7 \r\n" );
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document.write( "n = 3q - 14 = 3(7) - 14 = 21 - 14 = 7  \r\n" );
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document.write( "Substitute q = 7 and n = 7 in   \r\n" );
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document.write( "q + d + n = 18\r\n" );
document.write( "7 + d + 7 = 18\r\n" );
document.write( "   d + 14 = 18\r\n" );
document.write( "        d = 4\r\n" );
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document.write( "So 1 solution is 7 quarters, 7 nickels and 4 dimes\r\n" );
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document.write( "Substitute q = 8 \r\n" );
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document.write( "n = 3q - 14 = 3(8) - 14 = 24 - 14 = 10  \r\n" );
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document.write( "Substitute q = 8 and n = 10 in   \r\n" );
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document.write( "q + d +  n = 18\r\n" );
document.write( "8 + d + 10 = 18\r\n" );
document.write( "    d + 18 = 18\r\n" );
document.write( "         d = 0\r\n" );
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document.write( "So 1 solution is 8 quarters, 10 nickels and 0 dimes\r\n" );
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document.write( "We can't use 9 quarters for that's $2.25, and we'd\r\n" );
document.write( "have to make the remaining 25 cents with 9 nickels \r\n" );
document.write( "and dimes, which is impossible because even 9 \r\n" );
document.write( "nickels alone is 45 cents!!\r\n" );
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document.write( "So there are 4 solutions:\r\n" );
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document.write( "5 quarters, 1 nickel, and 12 dimes.           \r\n" );
document.write( "6 quarters, 4 nickels, and 8 dimes.\r\n" );
document.write( "7 quarters, 7 nickels, and 4 dimes.\r\n" );
document.write( "8 quarters, 10 nickels, and 0 dimes.\r\n" );
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document.write( "Edwin
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