Acme T-Shirt Company charges a $\$50$ set-up fee plus $\$9$ for  each shirt printed. Beta T-shirt Company has no set up fee, but charges $\$14$ per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?
I need to compare the costs of the two companies and find out when Acme is cheaper than Beta. Let me write an equation for the cost of each company. Let C_A be the cost for Acme and C_B be the cost for Beta. Then C_A = 50 + 9s, where s is the number of shirts. And C_B = 14s, since there is no set up fee. To find out when Acme is cheaper, I need to solve the inequality C_A < C_B. That means 50 + 9s < 14s. I can subtract 9s from both sides to get 50 < 5s. Then I can divide both sides by 5 to get 10 < s. This means that s has to be greater than 10 for Acme to be cheaper. The smallest integer that is greater than 10 is 11. So the minimum number of shirts for which a customer saves money by using Acme is 11. 