The average weight of A, B and C is $45$ kg. The average of A and B is $40$ kg, and the average of B and C is $43$ kg. Find B's weight.

**Set up the three equations.** $A + B + C = 3 \times 45 = 135$ We have $A + B = 2 \times 40$. So $A + B = 80$. $B + C = 2 \times 43 = 86$. **Isolate B.** $(A + B) + (B + C) = 80 + 86 = 166$, which equals $(A + B + C) + B = 135 + B$. **Solve.** $135 + B = 166 \Rightarrow B = 31$ kg. **Verification.** $A = 80 - 31 = 49$, $C = 86 - 31 = 55$, total $= 49 + 31 + 55 = 135$ ✓.