1. **State the problem:** Carl bought 19 apples of two varieties: Granny Smith and Gala. The total cost was 5.10. Granny Smith apples cost 0.25 each and Gala apples cost 0.30 each. We need to find how many of each type Carl bought. 2. **Define variables:** Let $x$ be the number of Granny Smith apples and $y$ be the number of Gala apples. 3. **Write equations:** - Total apples: $$x + y = 19$$ - Total cost: $$0.25x + 0.30y = 5.10$$ 4. **Solve the system:** From the first equation, express $y$: $$y = 19 - x$$ 5. Substitute into the cost equation: $$0.25x + 0.30(19 - x) = 5.10$$ 6. Distribute: $$0.25x + 5.70 - 0.30x = 5.10$$ 7. Combine like terms: $$\cancel{0.25x} - \cancel{0.30x} = -0.05x$$ $$-0.05x + 5.70 = 5.10$$ 8. Subtract 5.70 from both sides: $$-0.05x + \cancel{5.70} - \cancel{5.70} = 5.10 - 5.70$$ $$-0.05x = -0.60$$ 9. Divide both sides by -0.05: $$x = \frac{-0.60}{-0.05} = 12$$ 10. Find $y$: $$y = 19 - 12 = 7$$ **Answer:** Carl bought 12 Granny Smith apples and 7 Gala apples.