Question 1047240: How can I use thirty coins to equal $1?
Found 2 solutions by josmiceli, KMST:
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! It's obviously not
4 quarters
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The most you can get with
3 quarters is:
3 quarters + 25 pennies = 28 coins
not enough
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2 quarters + 10 nickels = 12 coins
not enough
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2 quarters + 5 nickels + 25 pennies = 32 coins
too many
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2 quarters + 3 nickels + 1 dime + 25 pennies = 31 coins
still too many
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2 quarters + 1 nickel + 2 dimes + 25 pennies = 30 coins
OK
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! Since  nickels make  ,
you will need to use some pennies.
The number of pennies used has to be a multiple of  ,
because, in cents, all the other coins amount to multiples of 5.
Could you do it with just pennies?
That would leave
to be made up with the other  coins.
Could we find 25 coins whose values add up to  cents?
cents is  nickels,
and  is not enough coins.
You cannot do it with only pennies.
Could you do it with exactly  pennies?
That would leave  cents to be made up
with the other  coins.
 cents is  nickels,
and  is not enough coins.
Could you do it with exactly  pennies?
That would leave  cents to be made up
with the other  coins.
 cents is  nickels,
and  is too many coins,
but that tells you
that with pennies,
you may be able to make up the remaining cents
with the extra coins you are allowed to use.
If you exchange  nickels for  dime,
you get the same amount, with  less coin.
So, if you do that twice, you end with
 nickels, and
 dimes,
along with the  pennies,
adding up to  coins,
and an amount, in cents, of
 (which is $1).
OTHER OPTIONS:
Could you use  pennies?
You would need to make up  cents
with the remaining  coins.
 cents would be  nickels.
That is too many coins.
You need  less coins.
If you get  dimes in exchange for  nickels<
you end up with:
 nickels, and
 dimes,
along with the  pennies,
adding up to  coins,
and an amount, in cents, of
 (which is $1).
Also with pennies, and starting from  nickels, you could instead,
get quarter in exchange for nickels,
to use  less coins,
and further reduce the number of coin
by getting dimes in exchange for  nickels.
That would leave you with
 quarter,
 dimes, and
 nickels,
along with the pennies,
adding up to  coins,
and an amount, in cents, of
 (which is $1).
Could you do it using exactly 25 pennies?
You would need to make up  cents
with the remaining  coins.
 nickels,
and that is  coins too many.
You already know that trading coins reduces the number
by each time you get quarter for nickels,
and by each time you get dime for nickels,
so getting quarters for nickels,
and dimes for nickels, you end up with
quarters,
dimes, and
 nickel,
along with the  pennies,
adding up to  coins,
and an amount, in cents, of
 (which is $1).
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