document.write( "Question 807682: 10 coins with 1.90 \n" ); document.write( "
Algebra.Com's Answer #486465 by Edwin McCravy(20077) $\"\"$ $\"About$
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document.write( "You couldn't have any pennies, because you'd have to have\r\n" );
document.write( "5 of them and you couldn't have the remaining $1.85 with 5 coins.\r\n" );
document.write( "You can't do that because even 5 quarters would be only $1.25, \r\n" );
document.write( "and even if you had 4 quarters and a half dollar, you'd have only \r\n" );
document.write( "$1.50. So there can be no pennies.\r\n" );
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document.write( "If you don't have any half dollars, the least number of quarters\r\n" );
document.write( "you could have would be 6, because if you had only 5 quarters, you'd\r\n" );
document.write( "have to make the remaining 65 cents with 5 coins.  You can't do that\r\n" );
document.write( "because even 5 dimes would only be 50 cents.\r\n" );
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document.write( "If you had 6 quarters, then you could make the remaining 40 cents\r\n" );
document.write( "with 4 dimes, and that would make 10 coins and that is one solution:\r\n" );
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document.write( "Solution #1:  6 quarters and 4 dimes\r\n" );
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document.write( "If you had 7 quarters, then you could make the remaining 15 cents\r\n" );
document.write( "with 3 nickels, and that would be another answer:\r\n" );
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document.write( "Solution #2:  7 quarters and 3 nickels\r\n" );
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document.write( "Now let's see if it's possible if we allow half dollars.  \r\n" );
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document.write( "Let's see if we can use 3 half dollars.  That would leave 40 cents \r\n" );
document.write( "to make with 7 coins.  If you use a quarter, that would leave 15c\r\n" );
document.write( "to make with 6 coins. Impossible.  If you didn't use a quarter, \r\n" );
document.write( "you'd have to have an even number of nickels.  2 nickels would \r\n" );
document.write( "leave 30 cents to make with 5 coins. Impossible.  4 nickels would \r\n" );
document.write( "leave 10 cents to make with 3 coins. Impossible. \r\n" );
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document.write( "Let's see if we can use 2 half dollars.  That would leave 90 cents \r\n" );
document.write( "to make with 8 coins.  If you use 2 quarters, that would leave 40\r\n" );
document.write( "cents to make with 6 coins, nickels and dimes only.  Impossible.\r\n" );
document.write( "3 quarters would leave 15 cents to make with 5 coins.  Impossible.\r\n" );
document.write( "So 2 half dollars is out.\r\n" );
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document.write( "Let's see if we can use just 1 half dollar.  That would leave $1.40\r\n" );
document.write( "to make with 9 coins.  We couldn't use 5 quarters, for that would\r\n" );
document.write( "leave 65 cents to make with 4 coins.  That's impossible because even 4\r\n" );
document.write( "dimes would only be 40 cents. If we used 4 quartersa, that would leave\r\n" );
document.write( "40 cents to make with 5 coins.  We can do that with 3 dimes and 2\r\n" );
document.write( "nickels.  So that the last solution:\r\n" );
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document.write( "Solution #3:  1 half dollar, 4 quarters, 3 dimes and 2 nickels.\r\n" );
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document.write( "So there are 3 solutions.\r\n" );
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document.write( "Edwin
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