Let's solve the problem step-by-step:
1. Understand the maximum allowable width in feet and inches:
The maximum width allowed between the windows is \(6 \frac{1}{2}\) feet. We need to convert this measurement to inches because the width of the bookshelf is given in inches.
[tex]\[6 \frac{1}{2} \text{ feet} = 6 + \frac{1}{2} \text{ feet}\][/tex]
[tex]\[6 \frac{1}{2} \text{ feet} = 6.5 \text{ feet}\][/tex]
Since 1 foot is equal to 12 inches, we convert 6.5 feet to inches:
[tex]\[6.5 \text{ feet} \times 12 \text{ inches/foot} = 78 \text{ inches}\][/tex]
2. Compare the bookshelf width to the maximum allowable width:
The width of the bookshelf Mrs. Aguilar purchased is given as 77 inches. We need to compare this with the maximum allowable width between the windows, which we have converted to 78 inches.
3. Calculate the difference:
[tex]\[78 \text{ inches (maximum allowable width)} - 77 \text{ inches (bookshelf width)} = 1 \text{ inch}\][/tex]
4. Interpret the result:
The bookshelf is 1 inch narrower than the maximum allowable space between the windows. This means the bookshelf will fit between the windows with 1 inch of space remaining.
Hence, the statement that accurately 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.
