1. **State the problem:** Two mechanics worked on a car. The first mechanic charges 115 per hour, the second charges 80 per hour. Together, they worked 20 hours and charged a total of 1775. We need to find how many hours each mechanic worked. 2. **Define variables:** Let $x$ be the hours worked by the first mechanic, and $y$ be the hours worked by the second mechanic. 3. **Write the system of equations:** - Total hours: $$x + y = 20$$ - Total charge: $$115x + 80y = 1775$$ 4. **Solve the system:** From the first equation, express $y$ as $$y = 20 - x$$ 5. Substitute into the second equation: $$115x + 80(20 - x) = 1775$$ 6. Simplify: $$115x + 1600 - 80x = 1775$$ $$35x + 1600 = 1775$$ 7. Subtract 1600 from both sides: $$35x = 175$$ 8. Divide both sides by 35: $$x = \frac{175}{35} = 5$$ 9. Find $y$: $$y = 20 - 5 = 15$$ 10. **Answer:** The first mechanic worked 5 hours, and the second mechanic worked 15 hours.