A weight of 8 N is located 10 cm from the fulcrum on the beam of a simple balance. What weight should be placed at 5 cm from the fulcrum on the opposite side in order to balance the system?

Have you learned how to calculate torque? If you use the fact that for a balance beam to be in equilibrium the sum of torques about the balance point must equal zero you should get the answer. Post back with your attempt and we'll help if you get stuck, but you must show us your work.