Let's analyze the problem step-by-step to determine if Mrs. Aguilar's bookshelf will fit between the windows.
1. Determine the required maximum width of the bookshelf to fit between the windows:
- The maximum width of the bookshelf to fit between the windows is given as [tex]\( 6 \frac{1}{2} \)[/tex] feet.
- Convert this measurement to inches because the bookshelf's width is given in inches.
- Since 1 foot is equal to 12 inches, convert [tex]\( 6 \frac{1}{2} \)[/tex] feet to inches:
[tex]\[
6 \frac{1}{2} \text{ feet} = 6.5 \text{ feet} \\
6.5 \text{ feet} \times 12 \text{ inches per foot} = 78 \text{ inches}
\][/tex]
2. Compare the width of the bookshelf to the maximum width allowed:
- The width of the bookshelf Mrs. Aguilar purchased is 77 inches.
- The distance between the windows is 78 inches.
3. Calculate the difference:
- The difference between the maximum width allowed and the bookshelf's width:
\[
78 \text{ inches} - 77 \text{ inches} = 1 \text{ inch}
- Since the difference is positive, the bookshelf will fit between the windows.
4. Interpret the difference:
- The result shows us that the bookshelf will fit between the windows with an additional 1 inch of remaining space.
Thus, the correct 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."
