Problem

Using his TightWad$($R$)$ database, Stu's MileageMiser has developed a new GPS based service to certify drivers for insurance discounts. He tracks their speeds, locations, and braking activity and delivers reports to insurance companies. January $1,2009$ he had $5,400$ paying customers. Of that group, a year later, $4,000$ were still customers. He spent $$10,600$ on programs designed to keep current customers happy and $$45,200$ on marketing to acquire new customers. His total number of customers on January $1,2010$ was $7,900.$ His revenue per customer is $$30$ per year and variable costs before marketing per customer are $$9$ per year. How many new customers did Stu acquire in $2009?$