1. **State the problem:** Ivan's weight is 4 kg more than Ethan's weight. Cael's weight is 5 kg less than Ivan's weight. The average weight of the three boys is 45 kg. 2. **Define variables:** Let Ethan's weight be $E$ kg. Then Ivan's weight is $E + 4$ kg. Cael's weight is $E + 4 - 5 = E - 1$ kg. 3. **Write the average formula:** The average weight of the three boys is given by $$\text{Average} = \frac{\text{Sum of weights}}{3}$$ 4. **Set up the equation:** $$45 = \frac{E + (E + 4) + (E - 1)}{3}$$ 5. **Simplify the numerator:** $$E + E + 4 + E - 1 = 3E + 3$$ 6. **Rewrite the equation:** $$45 = \frac{3E + 3}{3}$$ 7. **Multiply both sides by 3:** $$45 \times 3 = 3E + 3$$ $$135 = 3E + 3$$ 8. **Solve for $E$:** $$3E = 135 - 3$$ $$3E = 132$$ $$E = \frac{132}{3} = 44$$ 9. **Find the weights:** Ethan's weight $E = 44$ kg. Ivan's weight $= 44 + 4 = 48$ kg. Cael's weight $= 44 - 1 = 43$ kg. 10. **Check the average:** $$\frac{44 + 48 + 43}{3} = \frac{135}{3} = 45$$ **Final algebraic equation:** $$45 = \frac{E + (E + 4) + (E - 1)}{3}$$