document.write( "Question 1047240: How can I use thirty coins to equal $1?
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Algebra.Com's Answer #662739 by KMST(5328) $\"\"$ $\"About$

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Since $\"30\"$ nickels make $\"30%2A%28%22%240.05%22%29=%22%241.50%22\"$ ,
\n" ); document.write( "you will need to use some pennies.
\n" ); document.write( "The number of pennies used has to be a multiple of $\"5\"$ ,
\n" ); document.write( "because, in cents, all the other coins amount to multiples of 5.
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\n" ); document.write( "Could you do it with just $\"5\"$ pennies?
\n" ); document.write( "That would leave
\n" ); document.write( " $\"%22%241.00%22-%22%240.05%22=%22%240.95%22\"$
\n" ); document.write( "to be made up with the other $\"30-5=25\"$ coins.
\n" ); document.write( "Could we find 25 coins whose values add up to $\"95\"$ cents?
\n" ); document.write( " $\"95\"$ cents is $\"95%2F5=19\"$ nickels,
\n" ); document.write( "and $\"5+pennies+%2B+19+nickels=24+coins\"$ is not enough coins.
\n" ); document.write( "You cannot do it with only $\"5\"$ pennies.
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\n" ); document.write( "Could you do it with exactly $\"10\"$ pennies?
\n" ); document.write( "That would leave $\"100-10=90\"$ cents to be made up
\n" ); document.write( "with the other $\"30-10=20\"$ coins.
\n" ); document.write( " $\"90\"$ cents is $\"90%2F5=18\"$ nickels,
\n" ); document.write( "and $\"10+pennies+%2B+18+nickels=28+coins\"$ is not enough coins.
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\n" ); document.write( "Could you do it with exactly $\"15\"$ pennies?
\n" ); document.write( "That would leave $\"100-15=85\"$ cents to be made up
\n" ); document.write( "with the other $\"30-15=15\"$ coins.
\n" ); document.write( " $\"85\"$ cents is $\"85%2F5=17\"$ nickels,
\n" ); document.write( "and $\"15+pennies+%2B+17+nickels=32coins\"$ is too many coins,
\n" ); document.write( "but that tells you
\n" ); document.write( "that with $\"15\"$ pennies,
\n" ); document.write( "you may be able to make up the remaining $\"85\"$ cents
\n" ); document.write( "with the $\"15\"$ extra coins you are allowed to use.
\n" ); document.write( "If you exchange $\"2\"$ nickels for $\"1\"$ dime,
\n" ); document.write( "you get the same amount, with $\"2-1=1\"$ less coin.
\n" ); document.write( "So, if you do that twice, you end with
\n" ); document.write( " $\"17-2-2=highlight%2813%29\"$ nickels, and
\n" ); document.write( " $\"1%2B1=highlight%282%29\"$ dimes,
\n" ); document.write( "along with the $\"highlight%2815%29\"$ pennies,
\n" ); document.write( "adding up to $\"13%2B2%2B15=30\"$ coins,
\n" ); document.write( "and an amount, in cents, of
\n" ); document.write( " $\"15%2B13%2A5%2B2%2A10=15%2B65%2B20=100\"$ (which is $1).
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\n" ); document.write( "OTHER OPTIONS:
\n" ); document.write( "Could you use $\"20\"$ pennies?
\n" ); document.write( "You would need to make up $\"100-20=80\"$ cents
\n" ); document.write( "with the remaining $\"30-20=10\"$ coins.
\n" ); document.write( " $\"80\"$ cents would be $\"80%2F5=16\"$ nickels.
\n" ); document.write( "That is too many coins.
\n" ); document.write( "You need $\"16-10=6\"$ less coins.
\n" ); document.write( "If you get $\"6\"$ dimes in exchange for $\"12\"$ nickels<
\n" ); document.write( "you end up with:
\n" ); document.write( " $\"16-12=highlight%284%29\"$ nickels, and
\n" ); document.write( " $\"highlight%286%29\"$ dimes,
\n" ); document.write( "along with the $\"highlight%2820%29\"$ pennies,
\n" ); document.write( "adding up to $\"4%2B6%2B20=30\"$ coins,
\n" ); document.write( "and an amount, in cents, of
\n" ); document.write( " $\"20%2B4%2A5%2B6%2A10=20%2B20%2B60=100\"$ (which is $1).\r
\n" ); document.write( "\n" ); document.write( "Also with $\"20\"$ pennies, and starting from $\"16\"$ nickels, you could instead,
\n" ); document.write( "get $\"1\"$ quarter in exchange for $\"5\"$ nickels,
\n" ); document.write( "to use $\"5-1=4\"$ less coins,
\n" ); document.write( "and further reduce the number of coin
\n" ); document.write( "by getting $\"2\"$ dimes in exchange for $\"4\"$ nickels.
\n" ); document.write( "That would leave you with
\n" ); document.write( " $\"highlight%281%29\"$ quarter,
\n" ); document.write( " $\"highlight%282%29\"$ dimes, and
\n" ); document.write( " $\"16-5-4=highlight%287%29\"$ nickels,
\n" ); document.write( "along with the $\"highlight%2820%29\"$ pennies,
\n" ); document.write( "adding up to $\"1%2B2%2B7%2B20=30\"$ coins,
\n" ); document.write( "and an amount, in cents, of
\n" ); document.write( " $\"20%2B7%2A5%2B2%2A10%2B25=20%2B35%2B20%2B25=100\"$ (which is $1).
\n" ); document.write( "
\n" ); document.write( "Could you do it using exactly 25 pennies?
\n" ); document.write( "You would need to make up $\"100-25=75\"$ cents
\n" ); document.write( "with the remaining $\"30-25=5\"$ coins.
\n" ); document.write( " $\"75%7D%7D+cents+is+%7B%7B%7B75%2F5=15\"$ nickels,
\n" ); document.write( "and that is $\"15-5=10\"$ coins too many.
\n" ); document.write( "You already know that trading coins reduces the number
\n" ); document.write( "by $\"4\"$ each time you get $\"1\"$ quarter for $\"5\"$ nickels,
\n" ); document.write( "and by $\"1\"$ each time you get $\"1\"$ dime for $\"2\"$ nickels,
\n" ); document.write( "so getting $\"2\"$ quarters for $\"10\"$ nickels,
\n" ); document.write( "and $\"2\"$ dimes for $\"4\"$ nickels, you end up with
\n" ); document.write( " $\"highlight%282%29\"$ quarters,
\n" ); document.write( " $\"highlight%282%29\"$ dimes, and
\n" ); document.write( " $\"15-10-4=highlight%281%29\"$ nickel,
\n" ); document.write( "along with the $\"highlight%2825%29\"$ pennies,
\n" ); document.write( "adding up to $\"2%2B2%2B1%2B25=30\"$ coins,
\n" ); document.write( "and an amount, in cents, of
\n" ); document.write( " $\"2%2A25%2B2%2A10%2B5%2B25=50%2B20%2B5%2B25=100\"$ (which is $1). \n" ); document.write( "

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