Question 855432
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