In An Apartment Building, There Are 9 Apartments With Terraces For Every 16 Apartments. If The Apartment Building Has A Total Of 144 Apartments, How Many Apartments Have Terraces?

Feb 27, 2025 by ADMIN 180 views

Understanding the Problem

The problem presents a ratio of apartments with terraces to those without, which is 9:16. This means that for every 16 apartments without terraces, there are 9 apartments with terraces. The total number of apartments in the building is given as 144. We need to find out how many apartments have terraces.

Setting Up the Ratio

To solve this problem, we can set up a ratio using the given information. Let's assume that the number of apartments with terraces is 9x, where x is a multiplier. Since the ratio of apartments with terraces to those without is 9:16, the number of apartments without terraces is 16x.

Calculating the Total Number of Apartments

The total number of apartments in the building is the sum of the apartments with terraces and those without. We can set up an equation to represent this:

9x + 16x = 144

Solving for x

To solve for x, we can combine like terms and then divide both sides of the equation by the coefficient of x.

25x = 144

x = 144 / 25

x = 5.76

Calculating the Number of Apartments with Terraces

Now that we have the value of x, we can calculate the number of apartments with terraces by multiplying 9x.

Number of apartments with terraces = 9x = 9(5.76) = 51.84

Since we cannot have a fraction of an apartment, we can round down to the nearest whole number.

Number of apartments with terraces ≈ 51

Conclusion

In an apartment building with a total of 144 apartments, the ratio of apartments with terraces to those without is 9:16. Using this ratio, we can calculate the number of apartments with terraces by setting up a proportion and solving for x. The result is that approximately 51 apartments have terraces.

Additional Information

To verify our result, we can check if the number of apartments without terraces is indeed 16x.

Number of apartments without terraces = 16x = 16(5.76) = 92.16

Rounding down to the nearest whole number, we get:

Number of apartments without terraces ≈ 92

The total number of apartments is the sum of the apartments with terraces and those without:

Total number of apartments = 51 + 92 = 143

This is close to the given total of 144 apartments, which suggests that our calculation is accurate.

Real-World Applications

This problem can be applied to real-world scenarios, such as:

Urban planning: When designing a new apartment building, architects and urban planners need to consider the ratio of apartments with terraces to those without. This can affect the overall layout and design of the building.
Property management: Property managers need to know the number of apartments with terraces to determine the number of maintenance personnel required and to plan for outdoor maintenance tasks.
Marketing: Real estate agents and property developers can use the ratio of apartments with terraces to market the building and attract potential buyers.

Final Thoughts

In conclusion, the problem of finding the number of apartments with terraces in a building with a total of 144 apartments can be solved using a ratio and proportion. The result is that approximately 51 apartments have terraces. This problem can be applied to real-world scenarios, such as urban planning, property management, and marketing.

Understanding the Problem

Setting Up the Ratio

Calculating the Total Number of Apartments

The total number of apartments in the building is the sum of the apartments with terraces and those without. We can set up an equation to represent this:

9x + 16x = 144

Solving for x

To solve for x, we can combine like terms and then divide both sides of the equation by the coefficient of x.

25x = 144

x = 144 / 25

x = 5.76

Calculating the Number of Apartments with Terraces

Now that we have the value of x, we can calculate the number of apartments with terraces by multiplying 9x.

Number of apartments with terraces = 9x = 9(5.76) = 51.84

Since we cannot have a fraction of an apartment, we can round down to the nearest whole number.

Number of apartments with terraces ≈ 51

Conclusion

Additional Information

To verify our result, we can check if the number of apartments without terraces is indeed 16x.

Number of apartments without terraces = 16x = 16(5.76) = 92.16

Rounding down to the nearest whole number, we get:

Number of apartments without terraces ≈ 92

The total number of apartments is the sum of the apartments with terraces and those without:

Total number of apartments = 51 + 92 = 143

This is close to the given total of 144 apartments, which suggests that our calculation is accurate.

Real-World Applications

This problem can be applied to real-world scenarios, such as:

Urban planning: When designing a new apartment building, architects and urban planners need to consider the ratio of apartments with terraces to those without. This can affect the overall layout and design of the building.
Property management: Property managers need to know the number of apartments with terraces to determine the number of maintenance personnel required and to plan for outdoor maintenance tasks.
Marketing: Real estate agents and property developers can use the ratio of apartments with terraces to market the building and attract potential buyers.

Final Thoughts

Q&A

Q: What is the ratio of apartments with terraces to those without in the building?

A: The ratio of apartments with terraces to those without is 9:16.

Q: How many apartments with terraces are there in the building?

A: There are approximately 51 apartments with terraces in the building.

Q: How many apartments without terraces are there in the building?

A: There are approximately 92 apartments without terraces in the building.

Q: What is the total number of apartments in the building?

A: The total number of apartments in the building is 144.

Q: How can the ratio of apartments with terraces be applied in real-world scenarios?

A: The ratio of apartments with terraces can be applied in real-world scenarios such as urban planning, property management, and marketing.

Q: What is the significance of knowing the number of apartments with terraces in a building?

A: Knowing the number of apartments with terraces in a building is significant because it can affect the overall layout and design of the building, determine the number of maintenance personnel required, and be used to market the building.

Q: Can the ratio of apartments with terraces be used to calculate the number of apartments without terraces?

A: Yes, the ratio of apartments with terraces can be used to calculate the number of apartments without terraces by multiplying 16x.

Q: How can the total number of apartments in a building be calculated using the ratio of apartments with terraces?

A: The total number of apartments in a building can be calculated using the ratio of apartments with terraces by adding the number of apartments with terraces and those without.

Q: What is the relationship between the number of apartments with terraces and the total number of apartments in a building?

A: The number of apartments with terraces is a part of the total number of apartments in a building, and the ratio of apartments with terraces to those without can be used to calculate the number of apartments with terraces.

Q: Can the ratio of apartments with terraces be used to determine the number of maintenance personnel required?

A: Yes, the ratio of apartments with terraces can be used to determine the number of maintenance personnel required by considering the number of apartments with terraces and those without.

Q: How can the ratio of apartments with terraces be used to market a building?

A: The ratio of apartments with terraces can be used to market a building by highlighting the number of apartments with terraces and the benefits they offer.

Q: What is the significance of knowing the number of apartments without terraces in a building?

A: Knowing the number of apartments without terraces in a building is significant because it can affect the overall layout and design of the building, determine the number of maintenance personnel required, and be used to market the building.

Q: Can the ratio of apartments with terraces be used to calculate the number of apartments with terraces?

A: Yes, the ratio of apartments with terraces can be used to calculate the number of apartments with terraces by multiplying 9x.

Q: How can the ratio of apartments with terraces be used to determine the number of maintenance personnel required?

A: The ratio of apartments with terraces can be used to determine the number of maintenance personnel required by considering the number of apartments with terraces and those without.

Q: What is the relationship between the number of apartments without terraces and the total number of apartments in a building?

A: The number of apartments without terraces is a part of the total number of apartments in a building, and the ratio of apartments with terraces to those without can be used to calculate the number of apartments without terraces.

Q: Can the ratio of apartments with terraces be used to market a building?

A: Yes, the ratio of apartments with terraces can be used to market a building by highlighting the number of apartments with terraces and the benefits they offer.

Q: What is the significance of knowing the ratio of apartments with terraces to those without in a building?

A: Knowing the ratio of apartments with terraces to those without in a building is significant because it can affect the overall layout and design of the building, determine the number of maintenance personnel required, and be used to market the building.

Q: Can the ratio of apartments with terraces be used to calculate the total number of apartments in a building?

A: Yes, the ratio of apartments with terraces can be used to calculate the total number of apartments in a building by adding the number of apartments with terraces and those without.

Q: How can the ratio of apartments with terraces be used to determine the number of apartments with terraces?

A: The ratio of apartments with terraces can be used to determine the number of apartments with terraces by multiplying 9x.