1. **State the problem:** We need to find how many Combo A and Combo B lunches were sold given the total sandwiches and juices sold. 2. **Define variables:** Let $x$ be the number of Combo A sold and $y$ be the number of Combo B sold. 3. **Write equations based on the problem:** - Each Combo A has 1 sandwich and 2 juices, so sandwiches from Combo A: $x$, juices from Combo A: $2x$. - Each Combo B has 2 sandwiches and 1 juice, so sandwiches from Combo B: $2y$, juices from Combo B: $y$. 4. **Form the system of equations:** $$\begin{cases} x + 2y = 40 \\ 2x + y = 50 \end{cases}$$ 5. **Solve the system:** - From the first equation: $x = 40 - 2y$ - Substitute into the second equation: $$2(40 - 2y) + y = 50$$ $$80 - 4y + y = 50$$ $$80 - 3y = 50$$ $$-3y = 50 - 80$$ $$-3y = -30$$ $$y = 10$$ 6. **Find $x$:** $$x = 40 - 2(10) = 40 - 20 = 20$$ 7. **Answer:** The cafeteria sold 20 Combo A lunches and 10 Combo B lunches.