1. **State the problem:** Two thirds of the children were pediatricians, and 40 children were non-pediatricians. We need to find the total number of children. 2. **Set up the equation:** Let the total number of children be $x$. Since two thirds are pediatricians, the remaining one third are non-pediatricians. So, non-pediatricians = $\frac{1}{3}x$. 3. **Use the given information:** We know non-pediatricians = 40. Therefore, $$\frac{1}{3}x = 40$$ 4. **Solve for $x$:** Multiply both sides by 3 to isolate $x$. $$\cancel{3} \times \frac{1}{\cancel{3}} x = 40 \times 3$$ $$x = 120$$ 5. **Answer:** There are **120 children** in all.