The Total Number of Pillows Across All Floors

Oct 13, 2025 by wbrum.org 8 views

The Carrington Hotel's Colorful Makeover: A Mathematical Analysis

The Carrington Hotel, a renowned establishment, recently underwent a significant transformation with the help of a team of skilled interior designers. Their mission was to modernize the hotel's decor, and they achieved this by adding a unique touch to each floor. The designers placed 4 sofas on each of the 20 floors, and on each sofa, they carefully arranged $t$ tangerine pillows and $f$ fuchsia pillows. This intriguing setup has sparked the interest of mathematicians and enthusiasts alike, leading to a fascinating discussion about the total number of pillows and the potential implications of this design choice.

To begin, let's calculate the total number of pillows on each floor. Since there are 4 sofas on each floor, and each sofa has $t$ tangerine pillows and $f$ fuchsia pillows, the total number of pillows on each floor is:

4(t + f)

This expression represents the total number of pillows on each floor, taking into account both the tangerine and fuchsia pillows.

The Total Number of Pillows Across All Floors

Now, let's extend this calculation to the entire hotel, which consists of 20 floors. To find the total number of pillows across all floors, we multiply the number of pillows on each floor by the total number of floors:

20 \times 4(t + f)

This expression gives us the total number of pillows across all floors, providing a comprehensive understanding of the hotel's colorful makeover.

Simplifying the Expression

To simplify the expression, we can distribute the multiplication:

20 \times 4(t + f) = 80(t + f)

This simplified expression highlights the relationship between the total number of pillows and the number of floors, as well as the number of tangerine and fuchsia pillows.

The Total Number of Pillows: A Numerical Example

To illustrate the concept, let's consider a numerical example. Suppose the designers placed 5 tangerine pillows and 3 fuchsia pillows on each sofa. In this case, the total number of pillows on each floor would be:

4(5 + 3) = 4 \times 8 = 32

This means that each floor would have a total of 32 pillows.

The Total Number of Pillows Across All Floors: A Numerical Example

Now, let's extend this example to the entire hotel. With 20 floors, the total number of pillows across all floors would be:

20 \times 32 = 640

This numerical example demonstrates the application of the mathematical expression and provides a clear understanding of the total number of pillows in the hotel.

The Carrington Hotel's colorful makeover has sparked a fascinating discussion about the total number of pillows and the potential implications of this design choice. By applying mathematical concepts, we have calculated the total number of pillows on each floor and across all floors, providing a comprehensive understanding of the hotel's interior design. This analysis highlights the importance of mathematics in real-world applications and demonstrates the beauty of mathematical reasoning.

What is the total number of pillows on each floor if there are 3 tangerine pillows and 2 fuchsia pillows on each sofa?
If the hotel has 25 floors, what is the total number of pillows across all floors if there are 4 tangerine pillows and 3 fuchsia pillows on each sofa?
Suppose the designers placed 6 tangerine pillows and 4 fuchsia pillows on each sofa. What is the total number of pillows on each floor, and what is the total number of pillows across all floors?

The total number of pillows on each floor is $4(3 + 2) = 20$ .
The total number of pillows across all floors is $25 \times 4(4 + 3) = 25 \times 28 = 700$ .
The total number of pillows on each floor is $4(6 + 4) = 40$ . The total number of pillows across all floors is $20 \times 40 = 800$ .
The Carrington Hotel's Colorful Makeover: A Mathematical Analysis

In our previous article, we explored the mathematical concepts behind the Carrington Hotel's colorful makeover. We calculated the total number of pillows on each floor and across all floors, and we even provided some numerical examples to illustrate the concept. But we know that you, our readers, have questions! In this article, we'll address some of the most frequently asked questions about the hotel's decor and provide some additional insights into the math behind it.

Q: What is the total number of pillows on each floor if there are 5 tangerine pillows and 2 fuchsia pillows on each sofa?

A: To find the total number of pillows on each floor, we need to multiply the number of pillows on each sofa by the number of sofas on each floor. In this case, we have:

4(5 + 2) = 4 \times 7 = 28

So, the total number of pillows on each floor is 28.

Q: If the hotel has 25 floors, what is the total number of pillows across all floors if there are 3 tangerine pillows and 4 fuchsia pillows on each sofa?

A: To find the total number of pillows across all floors, we need to multiply the number of pillows on each floor by the total number of floors. In this case, we have:

25 \times 4(3 + 4) = 25 \times 4 \times 7 = 700

So, the total number of pillows across all floors is 700.

Q: What if the designers placed 6 tangerine pillows and 3 fuchsia pillows on each sofa? How many pillows would be on each floor, and how many would be across all floors?

A: To find the total number of pillows on each floor, we need to multiply the number of pillows on each sofa by the number of sofas on each floor. In this case, we have:

4(6 + 3) = 4 \times 9 = 36

So, the total number of pillows on each floor is 36.

To find the total number of pillows across all floors, we need to multiply the number of pillows on each floor by the total number of floors. In this case, we have:

20 \times 36 = 720

So, the total number of pillows across all floors is 720.

Q: Can you explain the concept of "tangerine" and "fuchsia" pillows in more detail?

A: Of course! In this context, "tangerine" and "fuchsia" refer to the colors of the pillows. Tangerine is a vibrant, orange-yellow color, while fuchsia is a bright, pink-purple color. The designers chose these colors to add a pop of color to the hotel's decor and create a unique and eye-catching atmosphere.

Q: How did the designers decide on the number of pillows to place on each sofa?

A: The designers likely used a combination of mathematical calculations and creative vision to determine the number of pillows to place on each sofa. They may have considered factors such as the size of the sofa, the color scheme of the room, and the overall aesthetic they wanted to achieve.

Q: Can you provide some additional examples of how the math behind the hotel's decor can be applied in real-world situations?

A: Absolutely! The math behind the hotel's decor can be applied in a variety of real-world situations, such as:

Designing a room with a specific color scheme and pattern
Creating a layout for a store or restaurant
Planning a event or party with a specific theme and decor
Even designing a garden or landscape with a specific color scheme and pattern!

The key is to understand the mathematical concepts behind the design and use them to create a unique and eye-catching atmosphere.

In this article, we've addressed some of the most frequently asked questions about the Carrington Hotel's colorful makeover and provided some additional insights into the math behind it. We hope this has been helpful in understanding the mathematical concepts behind the hotel's decor and has inspired you to think creatively about the math in your own life.