Subjects algebra

Bundle Usage 63C782

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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.