Window Proportions and Sizes

The question tells us that a house has 28 windows in total. These windows come in sizes of 2, 3, 4, or 5 feet. An important piece of information is that the number of windows of each size is proportional to their respective sizes. This means if we have 'k' as the constant of proportionality, the number of windows of size 2 feet is $2k$, size 3 feet is $3k$, size 4 feet is $4k$, and size 5 feet is $5k$.

Calculating the Proportionality Constant

The total number of windows is given as 28. We can set up an equation using the proportional numbers:

Number of windows of size 2 + Number of windows of size 3 + Number of windows of size 4 + Number of windows of size 5 = Total windows

Using our proportionality constant \(k\):

$$2k + 3k + 4k + 5k = 28$$

Combine the terms with \(k\):

$$(2 + 3 + 4 + 5)k = 28$$

$$14k = 28$$

Now, solve for \(k\):

$$k = \frac{28}{14}$$

$$k = 2$$

The constant of proportionality is 2.

Determining the Number of Windows of Each Size

Now that we have the value of \(k\), we can find the exact number of windows for each size:

• Windows of size 2 feet: \(2k = 2 \times 2 = 4\)
• Windows of size 3 feet: \(3k = 3 \times 2 = 6\)
• Windows of size 4 feet: \(4k = 4 \times 2 = 8\)
• Windows of size 5 feet: \(5k = 5 \times 2 = 10\)

Let's quickly check if these numbers add up to the total given windows:

$$4 + 6 + 8 + 10 = 28$$

This confirms our calculation for the number of windows of each size is correct.

Identifying Escape Windows

The problem states that the boy can escape through a window of size at least 4 feet. This means he can escape through windows that are 4 feet or larger.

Looking at the sizes available (2, 3, 4, 5 feet), the windows that are at least 4 feet are the ones of size 4 feet and size 5 feet.

Calculating the Number of Available Escape Windows

We need to sum the number of windows that are 4 feet and the number of windows that are 5 feet:

• Number of windows of size 4 feet = 8
• Number of windows of size 5 feet = 10

Total number of windows the boy can escape through is the sum of these two numbers:

$$8 + 10 = 18$$

Therefore, there are 18 windows available for the boy to escape through.