document.write( "Question 603441: Using only 22 coins, wich would you use to make $3.85? \n" ); document.write( "
Algebra.Com's Answer #380734 by AnlytcPhil(1806)\"\" \"About 
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document.write( "If we don't use any half dollars, then since 3.85/.25 = 15.4, the\r\n" );
document.write( "maximum number of quarters is 15.\r\n" );
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document.write( "If we use a total of q quarters then we have to make $3.85-$.25q with \r\n" );
document.write( "only 22-q coins.  The most amount of money 22-q coins can be is the \r\n" );
document.write( "amount when they are all dimes, so\r\n" );
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document.write( ".10(22-q) >= 385-.25q\r\n" );
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document.write( "Solving this gives\r\n" );
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document.write( "        q >= 11   \r\n" );
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document.write( "So the number of quarters is between 11 and 15\r\n" );
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document.write( "But if we use 15 quarters, that's $3.75 and we would have to make \r\n" );
document.write( "the remaining $.10 with 7 coins which is not possible.\r\n" );
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document.write( "If we use 14 quarters, that's $3.50 and we would have to make \r\n" );
document.write( "the remaining $.35 with 8 coins smaller than a quarter, which \r\n" );
document.write( "can only be done with 3 dimes and 5 pennies.  That's 1 way.\r\n" );
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document.write( "If we use 13 quarters, that's $3.25 and we would have to make \r\n" );
document.write( "the remaining $.60 with 9 coins smaller than a quarter, which \r\n" );
document.write( "can only be done with 3 dimes and 6 nickels. That's 1 way. \r\n" );
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document.write( "If we use 12 quarters, that's $3.00 and we would have to make \r\n" );
document.write( "the remaining $.85 with 10 coins smaller than a quarter, which \r\n" );
document.write( "can only be done with 7 dimes and 3 nickels. That's 1 way.\r\n" );
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document.write( "If we use 11 quarters, that's $2.75 and we would have to make \r\n" );
document.write( "the remaining $1.10 with 11 coins smaller than a quarter, which\r\n" );
document.write( " can only be done with 11 dimes. That's 1 way.\r\n" );
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document.write( "That's 4 ways using no half dollars.\r\n" );
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document.write( "It's a similar problem if we allow 1,2,3,4,5,6 or 7 half dollars.\r\n" );
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document.write( "If we use 1 half dollar then we have to make $3.35 with 21 coins.\r\n" );
document.write( "Proceding as above we get 4 ways for this too.\r\n" );
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document.write( "If we use 2 half dollar then we have to make $2.85 with 20 coins.\r\n" );
document.write( "Proceding as above we get 6 ways for this.\r\n" );
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document.write( "If we use 3 half dollar then we have to make $2.35 with 19 coins.\r\n" );
document.write( "Proceding as above we get 9 ways for this.\r\n" );
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document.write( "If we use 4 half dollar then we have to make $1.85 with 18 coins.\r\n" );
document.write( "Proceding as above we get 6 ways for this.\r\n" );
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document.write( "If we use 5 half dollar then we have to make $1.35 with 17 coins.\r\n" );
document.write( "Proceding as above we get 7 ways for this.\r\n" );
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document.write( "If we use 6 half dollar then we have to make $.85 with 16 coins.\r\n" );
document.write( "Proceding as above we get 5 ways for this.\r\n" );
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document.write( "If we use 7 half dollar then we have to make $.35 with 15 coins.\r\n" );
document.write( "Proceding as above there is only 1 ways for this, 5 nickels and 10\r\n" );
document.write( "pennies.\r\n" );
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document.write( "Total: 4+4+6+9+6+7+5+1 = 42\r\n" );
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document.write( "Edwin
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