jmc

Question

Alec must purchase 14 identical shirts and only has 130. There is a flat 2 entrance fee for shopping at the warehouse store where he plans to buy the shirts. The price of each shirt is the same whole-dollar amount. Assuming a 5% sales tax is added to the price of each shirt, what is the greatest possible price (in dollars) of a shirt that would allow Alec to buy the shirts?

Accepted Answer

The price of all the shirts without sales tax and the entrance fee must be at most (130-2)/1.05=121.91 dollars. Since Alec must buy 14 shirts, and since 121.91/148.71, the most each shirt can cost is 8 dollars.