1. State the problem: Two kinds of oil, Oil A costing 40 per liter and Oil B costing 70 per liter, are mixed to form 100 liters of mixture costing 5500. 2. Define variables: Let $x$ be the liters of Oil A and $y$ be the liters of Oil B. 3. Set up equations based on the problem: - Volume equation: $x + y = 100$ - Cost equation: $40x + 70y = 5500$ 4. Use substitution method: From the volume equation, solve for $y$: $$y = 100 - x$$ 5. Substitute $y$ into the cost equation: $$40x + 70(100 - x) = 5500$$ 6. Simplify and solve for $x$: $$40x + 7000 - 70x = 5500$$ $$-30x + 7000 = 5500$$ $$-30x = 5500 - 7000$$ $$-30x = -1500$$ $$x = \frac{-1500}{-30} = 50$$ 7. Find $y$ using $y = 100 - x$: $$y = 100 - 50 = 50$$ 8. Conclusion: 50 liters of Oil A and 50 liters of Oil B were used in the mixture.