A poultry farm sells eggs only by the carton and there are two types: 12-count cartons and 100-count cartons. The 12-unit carton is worth $a. The price of each egg in the 100-count cartons is 10% lower than the unit price of a 12-count carton. If a customer buys 360 eggs, how much did he pay?

360 = 3x100 + 5(12) The price of each egg for 12-count carton is $$ \frac{a}{12} $$ Then, the price of each egg for 100-count carton is$$ 0.9\times\frac{a}{12}=\frac{3a}{40} $$ Thus, the total price of the 360 eggs is $$ 3\times100\times\frac{3a}{40}+5\times12\times\frac{a}{12}=27.5a $$