#### Answer

40 haircuts

#### Work Step by Step

The first location's profit can be found by the number of haircuts, which will be h, times the cost of a haircut (45) minus the rent each month (1200) while the second location's profit is found by the number of haircuts (h) times the cost of a haircut (60) minus the rent each month (1800). Because we want to know when profits are equal to one another, we set the two equations equal to one another and solve for h.
45h-1200=60h-1800. Subtracting 60 to isolate h we get, -15h-1200=-1800. Adding 1200 to cancel 1200, we get -15h=-600. Dividing by -15 gives h=40.