To fit between two windows, the width of a bookshelf must be no greater than [tex]6 \frac{1}{2}[/tex] feet. Mrs. Aguilar purchases a bookshelf that is 77 inches wide. Which statement describes the relationship between the width of the bookshelf and the distance between the windows?

A. The bookshelf is 12 inches too wide to fit between the windows.
B. The bookshelf will fit between the windows with no extra room remaining.
C. The bookshelf will fit between the windows with 1 inch remaining.
D. The bookshelf is 5 inches too wide to fit between the windows.



Answer :

To solve this problem, let's go through the following steps:

### Step 1: Convert the width of the bookshelf from inches to feet.
The width of the bookshelf is given as 77 inches. To convert inches to feet, we use the conversion factor [tex]\(1 \text{ foot} = 12 \text{ inches}\)[/tex].

[tex]\[ \text{Width in feet} = \frac{77 \text{ inches}}{12 \text{ inches/foot}} = 6.416666667 \, \text{feet} \][/tex]

### Step 2: Determine the maximum allowable width in feet.
The maximum width allowed between the windows is [tex]\(6 \frac{1}{2} \)[/tex] feet, which is equivalent to:

[tex]\[ 6 \frac{1}{2} = 6.5 \, \text{feet} \][/tex]

### Step 3: Calculate the difference between the bookshelf width and the maximum allowable width.
[tex]\[ \text{Difference} = \text{Bookshelf width} - \text{Maximum allowable width} \][/tex]

[tex]\[ \text{Difference} = 6.416666667 \, \text{feet} - 6.5 \, \text{feet} = -0.083333333 \, \text{feet} \][/tex]

### Step 4: Convert this difference into inches.
Since [tex]\(1 \text{ foot} = 12 \text{ inches}\)[/tex], we convert feet to inches:

[tex]\[ \text{Difference in inches} = -0.083333333 \, \text{feet} \times 12 \, \text{inches/foot} = -0.999999996 \, \text{inches} \][/tex]

### Step 5: Interpret the result.
The difference we have found is approximately -1 inch. This indicates that the bookshelf is 1 inch less than the maximum allowable width.

### Conclusion
Given the interpretation of this result:
- The bookshelf is not too wide, so the first and fourth options are incorrect.
- The difference is not exactly zero, so the second option is also incorrect.
- Therefore, the correct interpretation is:

The bookshelf will fit between the windows with 1 inch remaining.