1. **State the problem:** A movie theater sells adult tickets at 12 each and child tickets at 8 each. On one night, 120 tickets were sold for a total of 1200. We need to find how many adult and child tickets were sold. 2. **Define variables:** Let $x$ be the number of adult tickets and $y$ be the number of child tickets. 3. **Set up equations:** - Total tickets sold: $$x + y = 120$$ - Total revenue: $$12x + 8y = 1200$$ 4. **Write the system in matrix form:** $$\begin{bmatrix}1 & 1 \\ 12 & 8\end{bmatrix} \begin{bmatrix}x \\ y\end{bmatrix} = \begin{bmatrix}120 \\ 1200\end{bmatrix}$$ 5. **Solve the system:** From the first equation, $$y = 120 - x$$. Substitute into the second: $$12x + 8(120 - x) = 1200$$ $$12x + 960 - 8x = 1200$$ $$4x + 960 = 1200$$ $$4x = 240$$ $$x = 60$$ 6. **Find $y$:** $$y = 120 - 60 = 60$$ 7. **Answer:** The theater sold 60 adult tickets and 60 child tickets.