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