The first floor of a house has a kitchen and dining room. The areas of the kitchen and dining room are in the ratio 2:1. The total area is 120 square feet.

What is the area of the kitchen?

What is the area of the dining room?

Let's call the area of the kitchen \( K \) and the area of the dining room \( D \). The problem states that the areas are in the ratio 2:1, meaning:

\[
K = 2D
\]

Additionally, the total area of the kitchen and dining room is 120 square feet, so:

\[
K + D = 120
\]

Substituting \( K = 2D \) into the second equation:

\[
2D + D = 120
\]

\[
3D = 120
\]

Solving for \( D \):

\[
D = \frac{120}{3} = 40 \, \text{square feet}
\]

Now, using \( K = 2D \):

\[
K = 2 \times 40 = 80 \, \text{square feet}
\]

### Final Answer:
- The area of the kitchen is **80 square feet**.
- The area of the dining room is **40 square feet**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. If the total area was 180 square feet, what would the areas of the kitchen and dining room be?
2. If the ratio were 3:1, what would the areas of the rooms be for a total area of 120 square feet?
3. How would the area distribution change if the total area increased by 50%?
4. What would be the new areas if the kitchen's area was doubled but the total area remained the same?
5. What if the ratio were reversed, and the dining room was twice as large as the kitchen?

**Tip:** When dealing with ratios, always try to express one variable in terms of the other for easier solving.

The first floor of a house has a kitchen and dining room. The areas of the kitchen and dining room are in the ratio 2:1. The total area is 120 square feet. What is the area of the kitchen? What is the area of the dining room?

Learn how to find the areas of a kitchen and dining room using ratios and algebra, given a total area of 120 square feet. This problem covers fundamental concepts in ratios and linear equations, making it ideal for students in Grades 6-8.

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