To determine the relationship between the width of the bookshelf and the distance between the windows, we need to assess whether the width of the bookshelf is more, less, or equal to the maximum width allowed to fit between the windows. Here are the detailed steps:
1. Convert the maximum allowable width from feet to inches:
- We are given that the maximum width allowed is [tex]\( 6 \frac{1}{2} \)[/tex] feet.
- First, we need to convert [tex]\( 6 \frac{1}{2} \)[/tex] feet into a decimal form: [tex]\( 6 + \frac{1}{2} = 6.5 \)[/tex] feet.
- Knowing that 1 foot is equal to 12 inches, we convert feet to inches: [tex]\( 6.5 \)[/tex] feet [tex]\( \times \)[/tex] 12 inches/foot [tex]\( = 78 \)[/tex] inches.
2. Compare the width of the bookshelf to the maximum allowable width:
- The width of the bookshelf is 77 inches.
- The maximum allowable width between the windows is 78 inches.
3. Calculate the difference between the bookshelf width and the maximum allowable width:
- Difference [tex]\( = 78 \text{ inches} - 77 \text{ inches} = 1 \text{ inch} \)[/tex].
This calculation tells us that the bookshelf is 1 inch narrower than the maximum allowable width.
4. Determine the relationship between the bookshelf width and the maximum allowable width:
- Since the bookshelf is 1 inch less than 78 inches, it means the bookshelf will fit between the windows.
- Additionally, there will be an extra 1 inch of space remaining once the bookshelf is placed.
Thus, the correct statement is:
The bookshelf will fit between the windows with 1 inch remaining.
