1. **State the problem:** Joan owes 440 for food and lodging and earns 1.25 for every 10 trees she plants. We need to find how many trees she must plant to break even, meaning her earnings equal her debt. 2. **Set up the equation:** Let $x$ be the number of trees Joan plants. Her earnings per tree are $\frac{1.25}{10} = 0.125$ per tree. The total earnings are $0.125x$. To break even, earnings equal debt: $$0.125x = 440$$ 3. **Solve for $x$:** $$x = \frac{440}{0.125}$$ 4. **Simplify the fraction:** $$x = \frac{440}{\cancel{0.125}} \times \frac{\cancel{8}}{1} = 440 \times 8$$ 5. **Calculate:** $$x = 3520$$ 6. **Interpretation:** Joan must plant 3520 trees to break even. **Note:** The handwritten note saying "342 trees" seems incorrect based on the given rates and debt.