1. **State the problem:** We are given two equations based on the cost of apples and berries: - Cost of 3 apples and 1 berry is 22 - Cost of 4 apples and 3 berries is 41 We need to find the cost of 7 apples. 2. **Define variables:** Let $a$ be the cost of one apple and $b$ be the cost of one berry. 3. **Write the system of equations:** $$3a + b = 22$$ $$4a + 3b = 41$$ 4. **Solve the system:** Multiply the first equation by 3 to align the $b$ terms: $$3(3a + b) = 3 \times 22$$ $$9a + 3b = 66$$ 5. **Subtract the second equation from this new equation:** $$\cancel{9a} + 3b - (\cancel{4a} + 3b) = 66 - 41$$ $$5a = 25$$ 6. **Solve for $a$:** $$a = \frac{25}{5} = 5$$ 7. **Find the cost of 7 apples:** $$7a = 7 \times 5 = 35$$ **Final answer:** The cost of 7 apples is $35$.