1. **Problem statement:** Helmut earns 25 euros for 2.5 hours of work. We want to find out how much he earns after 12 hours. 2. **Formula and rule:** Since the pay is proportional to the hours worked, we use the rule of three (proportionality): $$\frac{\text{Gehalt}_1}{\text{Arbeitszeit}_1} = \frac{\text{Gehalt}_2}{\text{Arbeitszeit}_2}$$ 3. **Set up the proportion:** $$\frac{25}{2.5} = \frac{x}{12}$$ where $x$ is the unknown salary for 12 hours. 4. **Solve for $x$:** Multiply both sides by 12: $$x = \frac{25}{2.5} \times 12$$ 5. **Simplify the fraction:** $$\frac{25}{2.5} = \frac{\cancel{25}}{\cancel{2.5}} = 10$$ 6. **Calculate the final amount:** $$x = 10 \times 12 = 120$$ 7. **Answer:** Helmut earns **120 euros** after 12 hours of work.