The local grocery store rents carpet cleaners for $45 per day and sells shampoo

Question

The local grocery store rents carpet cleaners for $45 per day and sells shampoo to go with the cleaner for $12. To purchase a carpet cleaner it would cost $350 with the corresponding shampoo costing $10. The last time you cleaned your carpets, it took 2 shampoo bottles that worked with the rental cleaner. Cleaning the same amount of carpet with the purchased cleaner would use 3 bottles of the corresponding shampoo. How many times would you have to clean the carpet in your house to make buying a carpet cleaner cheaper than renting one?

Explanation / Answer

Cost of one carpet cleaing using Rental

= 45+2*12 = 45+24 = 69

Cost of purachsed claener = 350

Cost of cleaning = 3*10 = 30

Let X be the no of times carpet is cleaned.

So For equal cost, 69X = 350+30X

ie 39X = 350

ie X= 9 times.

So If Carpet is cleaned more than 9 times, buying a carpet cleaner will be cheaper.

Check:

Cost of 9 Rentals = 9*69 = 621

Cost of purchaed for 9 cleaning = 350+9*30 = 620

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