To determine whether Mrs. Aguilar's 77-inch-wide bookshelf will fit between the windows, we need to compare the width of the bookshelf to the maximum allowable width for it to fit.
1. Convert the maximum width from feet and inches to inches:
- The maximum width allowed is [tex]\(6 \frac{1}{2}\)[/tex] feet.
- First, convert the feet to inches:
- 6 feet = [tex]\(6 \times 12 = 72\)[/tex] inches.
- Next, convert the half foot to inches:
- [tex]\(\frac{1}{2}\)[/tex] foot = [tex]\( \frac{1}{2} \times 12 = 6\)[/tex] inches.
- Add these two values together to get the total maximum width in inches:
- [tex]\(72\)[/tex] inches (from the 6 feet) + [tex]\(6\)[/tex] inches (from the [tex]\(\frac{1}{2}\)[/tex] foot) = [tex]\(78\)[/tex] inches.
Thus, the maximum width that the bookshelf can be to fit between the windows is 78 inches.
2. Compare the width of the bookshelf to the maximum allowable width:
- The width of the bookshelf: 77 inches.
- The maximum allowable width: 78 inches.
- Determine the difference between the width of the bookshelf and the maximum allowable width:
- Difference = [tex]\(78 - 77 = 1\)[/tex] inch.
Since the difference is 1 inch, 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."
