Part A)
Total costs $52,000
Each day spends $680 and earns $960
Let d be the number of days
So the total number of spending days plus total cost has to be less than the total number of earnings for her make profit.
680d + 52,000 <= 960d
Part B)
Solve the equation above
680d + 52,000 <= 960d
52,000 <= 960d - 680d
52,000 < = 280d
52,000 / 280 <= d
185.7 < d
or
d > 185.7
So Julianne will begin making profit at 188 days.