Question 941837: A set of 10 coins may contain any combination of 1c, 5c, 10c, 20c, or 50c coins. In how many different ways can the set of 10 coins have a total value of 59c?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
Since 59 ends with 9, we must use either 4 or 9 1c coins.
The only way we can use 9 1c coins, is 1 50c coin and 9 1c coins.
And that is the only way we can use a 50c coin.
1. So that's 1 way, 1 50c coin and 9 1c coins.
For any other ways we must use no 50c coins and 4 1c coins, so we must
mave 55c with 6 coins.
We can't use 2 20c coins because that would mean having 15c with
4 coins, using 10c and 5c coins, which cannot be done.
If we use 1 20c coin, we must have 35c in 5 coins, which could only
be had with 2 10c coins and 3 5c coins.
2. So that's a second way, 1 20c coin, 2 10c coins, 1 5c coin, and,
of course, 4 1c coins.
If we don't use any 50c or 20c coins, we must have 55C in 6 5c and 10c
coins. Since 55c ends in a 5, we must have 1 5c coin, so we put that
aside and get the remaining 50c with 5 coins, which we can do by using
5 10c coins.
3. So that's the third way, 1 5c coin and 5 10c coins, and, of course,
4 1c coins.
Answer: 3 ways.
Edwin
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