Chapter 1.1, Problem 56E

Equipment rental. The local supermarket rents carpet cleaners for $\text{\$20}$ a day. These cleaners use shampoo in a special cartridge that sells for $\text{\$16}$ and is available only from the super- market. A home carpet cleaner can be purchased for $\text{\$300}$. Shampoo for the home cleaner is readily available for $\text{\$9}$ a bottle. Past experience has shown that it takes two shampoo cartridges to clean the 10-foot-by-12-foot carpet in your living room with the rented cleaner. Cleaning the same area with the home cleaner will consume three bottles of shampoo. If you buy the home cleaner, how many times must you clean the living-room carpet to make buying cheaper than renting?