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.
### 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.
