1. **State the problem:** We have two types of bundles: Bundle A with 2 hours preproduction and 1 hour postproduction, and Bundle B with 1 hour preproduction and 3 hours postproduction. The studio uses 7 bundles total, with 11 hours preproduction and 13 hours postproduction. We need to find how many of each bundle are used.
2. **Define variables:** Let $x$ be the number of Bundle A used, and $y$ be the number of Bundle B used.
3. **Write the system of equations:**
$$\begin{cases} x + y = 7 \\ 2x + y = 11 \\ x + 3y = 13 \end{cases}$$
4. **Solve the system:** From the first equation, express $y$:
$$y = 7 - x$$
5. Substitute $y$ into the second equation:
$$2x + (7 - x) = 11$$
$$2x + 7 - x = 11$$
$$x + 7 = 11$$
$$x = 11 - 7 = 4$$
6. Substitute $x=4$ into $y = 7 - x$:
$$y = 7 - 4 = 3$$
7. **Check with the third equation:**
$$x + 3y = 4 + 3 \times 3 = 4 + 9 = 13$$
This matches the given postproduction hours.
8. **Answer:** The studio uses 4 bundles of type A and 3 bundles of type B.
Bundle Usage 63C782
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