Question 855432: Suppose you have a currency called miso in three denominations, 1 miso, 10misos and 50 misos. In how many ways can you pay a bill of 107 misos
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! Let's do this logically.
What is the largest number of 50s that you can use? 2 (50*2=100; any more would be over the total). The possibilities are those that use 0-50s, 1-50 or 2-50s. We'll do the 2s first because there's only possibility: take 2-50s from 107 and you have 7 leftover. Those will have to be paid by 1s.
Possibility with 2-50: 50,50,1,1,1,1,1,1,1
How about if you're using 1-50? The remainder would be 57. How many ways can you make 57?
Possibilities with 1-50:
50,10,10,10,10,10,1,1,1,1,1,1,1
50,10,10,10,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
50,10,10,10,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
50,10,10 (+37 ones)
50,10 (+47 ones)
50 +57 ones
Possibilities with 0-50s:
10,10,10,10,10,10,10,10,10,10 +7 ones
10,10,10,10,10,10,10,10,10 +17ones
10,10,10,10,10,10,10,10 +27 ones
10,10,10,10,10,10,10 +37 ones
10,10,10,10,10,10 +47 ones
10,10,10,10,10 +57 ones
10,10,10,10 +67 ones
10,10,10 +77 ones
10,10 +87 ones
10 + 97 ones
107 ones
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