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The problem provided involves a system of linear equations. Let's break it down step by step:

### Variables:
Let:
- \( x \) = number of trucks (camiones) produced,
- \( y \) = number of puppets (marionetas) produced,
- \( z \) = number of puzzles (rompecabezas) produced.

### Constraints:

1. **Wood requirement (in kilograms)**:
   - Each truck requires 2 kg of wood,
   - Each puppet requires 0.5 kg of wood (500 grams),
   - Each puzzle requires 0.8 kg of wood (800 grams),
   - In total, 91 kg of wood is used.

   This gives us the first equation:
   \[
   2x + 0.5y + 0.8z = 91
   \]

2. **Labor hours requirement**:
   - Each truck requires 3 hours of labor,
   - Each puppet requires 4 hours of labor,
   - Each puzzle requires 3.5 hours of labor,
   - In total, 313 hours of labor are used.

   This gives us the second equation:
   \[
   3x + 4y + 3.5z = 313
   \]

3. **Total number of toys**:
   - The company produced a total of 89 toys (trucks, puppets, and puzzles combined).

   This gives us the third equation:
   \[
   x + y + z = 89
   \]

### System of Equations:
We now have the following system:
1. \( 2x + 0.5y + 0.8z = 91 \)
2. \( 3x + 4y + 3.5z = 313 \)
3. \( x + y + z = 89 \)

I will now solve this system to find the values of \( x \), \( y \), and \( z \).The solution to the system of equations is:

- \( x = 23 \) trucks,
- \( y = 26 \) puppets,
- \( z = 40 \) puzzles.

Thus, the company produced **23 trucks**, **26 puppets**, and **40 puzzles**.

Would you like a detailed explanation of how the system was solved, or do you have any further questions?

Here are 5 related questions you might consider:
1. How would the solution change if the total number of toys was different?
2. What if the labor hours for producing each toy were altered?
3. How does the wood requirement affect the number of toys produced?
4. Can you solve this system graphically, and how would that look?
5. What would happen if the company decided to double the production of one type of toy?

**Tip**: When solving systems of equations, try expressing one variable in terms of others to simplify the process.

Una fábrica de juguetes artesanales produce camiones, marionetas y rompecabezas de madera. Para fabricar un camión se necesita 2 kg de madera y 3 horas de trabajo, mientras que para una marioneta se necesita 500 g de madera y 4 horas de trabajo. Los rompecabezas necesitan 800 g de madera y 3.5 horas de trabajo. Durante una semana, la empresa ha puesto en el mercado 89 juguetes utilizando 91 kg de madera y 313 horas de trabajo. Determina el número de camiones, marionetas y rompecabezas producidos.

This math problem involves solving a system of linear equations to determine the number of trucks (camiones), puppets (marionetas), and puzzles (rompecabezas) produced in a week, based on wood and labor constraints. Explore key algebraic techniques in this detailed solution for students in grades 10-12.

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