1. **State the problem:** An electronic weighing scale balances two batteries and one casing with eight screens. Also, one battery balances one casing and one screen. We need to find how many screens balance one battery. 2. **Define variables:** Let $B$ = weight of one battery, $C$ = weight of one casing, and $S$ = weight of one screen. 3. **Write equations from the problem:** - Two batteries and one casing balance eight screens: $$2B + C = 8S$$ - One battery balances one casing and one screen: $$B = C + S$$ 4. **Express $C$ from the second equation:** $$C = B - S$$ 5. **Substitute $C$ into the first equation:** $$2B + (B - S) = 8S$$ $$2B + B - S = 8S$$ $$3B - S = 8S$$ 6. **Simplify:** $$3B = 9S$$ 7. **Divide both sides by 3:** $$\cancel{3}B = \cancel{3}3S$$ $$B = 3S$$ 8. **Interpretation:** One battery balances three screens. **Final answer:** 3