9514 1404 393
Answer:
47
Step-by-step explanation:
There are 4 distinct coin values. The numbers of these are 2, 3, 1, 2. Adding 1 to this set gives us 3, 4, 2, 3, and the product of these numbers is 72.
This is the number of distinct subsets of the coins. However, even though a subset of the coins may be distinct, it may still have the same monetary value as another subset. There are 24 values that can be formed two ways:
10, 11, 12, 15, 16, 17, 25, 26, 27, 35, 36, 37,
40, 41, 42, 50, 51, 52, 60, 61, 62, 65, 66, 67
In general, these involve replacing a dime with 2 nickels, or a quarter with a dime and 3 nickels.
So, removing the value of 0 from the list of 72 possible values, along with these 24 duplicates, leaves a total of 47 different sums of money.
__
Those sums are ...
1, 2, 5, 6, 7, 10, 11, 12, 15, 16, 17, 20,
21, 22, 25, 26, 27, 30, 31, 32, 35, 36, 37, 40,
41, 42, 45, 46, 47, 50, 51, 52, 55, 56, 57, 60,
61, 62, 65, 66, 67, 70, 71, 72, 75, 76, 77
