To determine whether the bookshelf will fit between the two windows and how much room (or lack thereof) it will have, one needs to follow these steps:
1. Convert the distance requirement from feet to inches:
- We need to convert the width constraint from feet to inches because the bookshelf's width is given in inches.
- The width requirement is [tex]\(6 \frac{1}{2}\)[/tex] feet.
- To convert [tex]\(6 \frac{1}{2}\)[/tex] feet to inches, recall that 1 foot = 12 inches. Therefore:
[tex]\[
6 \frac{1}{2} \text{ feet} = 6.5 \text{ feet} = 6.5 \times 12 \text{ inches} = 78 \text{ inches}
\][/tex]
2. Compare the bookshelf width with the converted distance:
- The width of the bookshelf is 77 inches.
- We need to see how this 77-inch wide bookshelf compares to the 78-inch distance available between the windows.
3. Calculate the difference:
- Calculate the difference between the distance available between the windows (78 inches) and the width of the bookshelf (77 inches):
[tex]\[
\text{Difference} = 78 \text{ inches} - 77 \text{ inches} = 1 \text{ inch}
\][/tex]
Since the difference is positive and equals 1 inch, this signifies that the bookshelf will fit between the windows with 1 inch remaining.
4. Select the appropriate statement:
Given the calculations, the statement that best describes the relationship between the width of the bookshelf and the distance between the windows is:
- "The bookshelf will fit between the windows with 1 inch remaining."
Thus, the correct statement is:
- The bookshelf will fit between the windows with 1 inch remaining.
