1. **State the problem:** We want to find the cost of 1 fruit cake and 4 muffins given two purchase scenarios. 2. **Define variables:** Let $x$ be the cost of 1 fruit cake and $y$ be the cost of 1 muffin. 3. **Write the system of equations from the problem:** $$3x + 5y = 33.5$$ $$4x + 15y = 58$$ 4. **Solve the system:** Multiply the first equation by 3 to align the $y$ terms: $$3(3x + 5y) = 3(33.5) \Rightarrow 9x + 15y = 100.5$$ 5. **Subtract the second equation from this new equation:** $$\cancel{9x} + 15y - (\cancel{4x} + 15y) = 100.5 - 58$$ $$5x = 42.5$$ 6. **Solve for $x$:** $$x = \frac{42.5}{5} = 8.5$$ 7. **Substitute $x=8.5$ into the first equation:** $$3(8.5) + 5y = 33.5$$ $$25.5 + 5y = 33.5$$ 8. **Isolate $y$:** $$5y = 33.5 - 25.5 = 8$$ $$y = \frac{8}{5} = 1.6$$ 9. **Calculate the cost of 1 fruit cake and 4 muffins:** $$x + 4y = 8.5 + 4(1.6) = 8.5 + 6.4 = 14.9$$ **Final answer:** You pay 14.9 euros for 1 fruit cake and 4 muffins.