There is no binary equation, which is a bit complicated to calculate, but in fact, the principle is the same as the binary equation:

Suppose that the cost of purchasing new equipment is X, the service fee is 1%X, the service fee of selling goods is 278- 1%X, and the service fee of selling goods accounts for 3% of the total amount of selling goods, then the sales amount is =(278- 1%X)/3%, and the customer breaks even, so the sales amount of goods is just used to pay the service fee. After sorting, we get 27800/3-278-4/3X=0, X=674 1.5, so we need 674 1.5 yuan to buy new equipment.