x+y+z = 7
9x+7y+5z = 53
=> x-z = 2 and 2x+y = 9
since he had all the days atleast once, therefore x>2 and x<6
so the possible values of x are (5,4,3)
x = 5 will not satisfy 2x+y = 9 as y would be negative.
so, x= (4,3) y=(1,3) z=(2,1)..
possible solutions = (4,1,2) and (3,3,1)