Determining the Area of the Dining Room After Remodeling

This article explains a mathematical problem and provides a detailed process to determine the area of the dining room after a family room has undergone remodeling. The problem involves understanding ratios, area calculations, and algebraic equations to find the solution.

The problem we face is to determine the area of the dining room after the family room has been remodeled. We are given the following information:

The ratio of the area of the dining room to the family room is 2:3. After remodeling, the family room became half its original size, and it is now 60 square feet less than the dining room.

Step-by-Step Calculation

Let's denote the total floor space as x square feet.

Initial Areas

From the given ratio 2:3, we know:

Dining room area (d) 2 / 5 x

Family room area (f) 3 / 5 x

After Remodeling

After remodeling, the family room has become half its original size:

Family room area after remodeling (f') 1 / 2 fx 3 / 10 x

Therefore, the dining room area after remodeling (d') is:

Dining room area after remodeling (d') x - 3 / 10 x 7 / 10 x

Given that the difference in area is 60 square feet, we can write:

Difference in area 7 / 10 x - 3 / 10 x 4/10 x

Thus:

4 / 10 x 60 square feet

From which we can solve for x:

x 60 * 10 / 4 150 square feet

Now, we can calculate the area of the dining room after remodeling:

Dining room area after remodeling (d') 7 / 10 * 150 105 square feet

Conclusion

The area of the dining room after the family room has been remodeled is 105 square feet. Understanding the relationship between the areas and applying basic mathematical principles allowed us to reach this conclusion accurately.

Understanding the Problem

The problem involves a combination of ratio understanding and area calculations. By breaking down the information given and analyzing the relationships, we can solve the problem step by step. This method ensures that every detail is accounted for, leading to a precise answer.

Implications for Home Remodeling

This example highlights the importance of considering space ratios and area changes during the remodeling process. Accurate area calculations can help in planning and executing home renovation projects effectively, ensuring that the living spaces meet the desired aesthetic and functional requirements.