"my mathematical brain hates that I need to round this"

It isn't rounding, casting to int chops the decimal bit off.

I'm expecting no because you can't make 75 with two notes of 50

Am I being thick? I put this in for the test case: {25, 25, 50, 50, 100};

Expected: "YES"
But was: "NO"

Why is "YES" expected?
25 goes in till, one 25 bill change - YES
25 goes in till, two 25 bills change - YES
50 goes in till, one 25 bill change and one 50 bill change - YES (minus one 25 bill change)
50 goes in till, two 50 bill change - YES (minus one 25 bill change)
100 can't go in till, the two 50 bills can't make the 75 required change?