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The problem states the following:

- The surface area of the living room is three times the surface area of the kitchen.
- There are 5 bedrooms, each having 4 m² less surface area than the kitchen.
- The total surface area of all these rooms (living room + 5 bedrooms) is 106 m².

Let the surface area of the kitchen be \( x \) m².

### Step-by-step calculation:

1. The surface area of the living room is \( 3x \) m² (three times the kitchen).
2. Each bedroom has a surface area of \( x - 4 \) m², and there are 5 bedrooms. So, the total surface area of the bedrooms is:
   \[
   5(x - 4)
   \]
3. The total surface area is given as 106 m². So, the equation becomes:
   \[
   3x + 5(x - 4) = 106
   \]
4. Expand the equation:
   \[
   3x + 5x - 20 = 106
   \]
5. Combine like terms:
   \[
   8x - 20 = 106
   \]
6. Add 20 to both sides:
   \[
   8x = 126
   \]
7. Solve for \( x \):
   \[
   x = \frac{126}{8} = 15.75
   \]

Thus, the surface area of the kitchen is **15.75 m²**.

Would you like further clarification or details on this?

Here are some related questions to expand on this:

1. What would the total surface area be if the living room were four times the size of the kitchen instead?
2. How would the equation change if there were only 4 bedrooms?
3. What is the surface area of each bedroom based on the current solution?
4. How can we calculate the total surface area if we know only the area of one room?
5. What happens if the total surface area is increased to 120 m² but the rest of the conditions remain the same?

**Tip:** Always ensure the units are consistent throughout the problem to avoid errors.

De oppervlakte van onze living is net het drievoud van de oppervlakte van onze keuken. De 5 slaapkamers zijn elk 4 m² minder dan de keuken. De totale oppervlakte van al deze ruimtes is 106 m². Wat is de oppervlakte van de keuken?

Learn how to calculate the surface area of a kitchen based on the total surface area of other rooms. The living room is three times the size of the kitchen, and five bedrooms are each 4 m² smaller than the kitchen. This problem involves algebraic concepts suitable for students in Grades 6-8.

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