1. **State the problem:** A tree surgeon finds that 3 out of every 10 ash trees inspected have ash die-back disease and must be felled. She fells 45 ash trees. We need to find how many healthy trees she leaves standing. 2. **Identify the ratio:** The ratio of diseased trees to total trees is $\frac{3}{10}$. 3. **Find total trees inspected:** Let the total number of trees inspected be $x$. Since $\frac{3}{10}$ of them are diseased and felled, we have: $$\frac{3}{10}x = 45$$ 4. **Solve for $x$:** $$x = \frac{45 \times 10}{3}$$ $$x = \frac{450}{3}$$ $$x = 150$$ 5. **Calculate healthy trees:** Healthy trees are the remaining $\frac{7}{10}$ of the total: $$\frac{7}{10} \times 150 = 7 \times 15 = 105$$ 6. **Answer:** The tree surgeon leaves standing **105 healthy ash trees**.