To determine which statement accurately describes the relationship between the width of the bookshelf and the distance between the windows, we need to follow these steps:
1. Convert the maximum allowed width from feet to inches:
- The maximum width the bookshelf can be to fit between the windows is [tex]\( 6 \frac{1}{2} \)[/tex] feet.
- Converting this to inches: [tex]\( 6 \frac{1}{2} \)[/tex] feet is equivalent to [tex]\( 6.5 \)[/tex] feet.
- Since there are 12 inches in a foot, multiply the number of feet by 12 to convert to inches:
[tex]\[
6.5 \times 12 = 78 \text{ inches}
\][/tex]
2. Compare the width of the purchased bookshelf with the maximum allowed width:
- The width of the purchased bookshelf is given as 77 inches.
- The maximum allowed width is 78 inches (from our conversion above).
3. Calculate the difference between the maximum allowed width and the actual width of the bookshelf:
- Subtract the width of the bookshelf from the maximum allowed width:
[tex]\[
78 \text{ inches} - 77 \text{ inches} = 1 \text{ inch}
\][/tex]
- This result tells us that the purchased bookshelf is 1 inch narrower than the maximum allowable width between the windows.
4. Determine the correct statement based on the difference:
- Since the bookshelf is 1 inch narrower than the maximum width, it will fit between the windows with 1 inch remaining.
Thus, the statement that 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."
