A social agency is charged with providing services to three types of clients: A, B, and C. A total of 500 clients are to be served, with $150,000 available for counseling and $100,000 available for emergency food and shelter. Type A clients require an average of $200 for counseling and $300 for emergencies, type B clients require an average of $500 for counseling and $200 for emergencies, and type C clients require an average of $300 for counseling and $100 for emergencies. How many of each type of client can be served?
Application problems require systems of equations in three variables.