SOLUTION: How can I use thirty coins to equal $1?

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
------------------
The most you can get with
3 quarters is:
3 quarters + 25 pennies = 28 coins
not enough
------------------
2 quarters + 10 nickels = 12 coins
not enough
------------------
2 quarters + 5 nickels + 25 pennies = 32 coins
too many
------------------
2 quarters + 3 nickels + 1 dime + 25 pennies = 31 coins
still too many
------------------
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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