The answer is 18.
He has 575 cents.
25q + 5n = 575
q + n = 43
(575-q*25)/5=n
Listing some points in the form (q,n), until we find that q+n is 43:
(0,115); q+n=115
(1,110); q+n=111
(2,105); q+n=107
(3,100); q+n=103
(4,95); q+n=99
(5,90); q+n=95
(6,85); q+n=91
(7,80); q+n=87
(8,75); q+n=83
(9,70); q+n=79
(10,65); q+n=75
(11,60); q+n=71
(12,55); q+n=67
(13,50); q+n=63
(14,45); q+n=59
(15,40); q+n=55
(16,35); q+n=51
(17,30); q+n=47
(18,25); q+n=43
(19,20); q+n=39
(20,15); q+n=35
(21,10); q+n=31
(22,5); q+n=27
(23,0); q+n=23
(24,-5); q+n=19
When q+n is 43, he had 18 quarters!
18*25+(43-18)*5=575
There was a much easier way to do this.
