Answered

To fit between two windows, the width of a bookshelf must be no greater than $6 \frac{1}{2}$ 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?


AThe bookshelf is 12 inches too wide to fit between the windows.
BThe bookshelf will fit between the windows with no extra room remaining.
CThe bookshelf will fit between the windows with 1 inch remaining.
DThe bookshelf is 5 inches too wide to fit between the windows.

Verified Answer :

  • Convert the maximum allowed width of \(6 \frac{1}{2}\) feet to inches by multiplying by \(12\), resulting in \(78\) inches.
  • Compare the bookshelf width (\(77\) inches) to the space width (\(78\) inches).
  • Calculate the difference, which is \(78 - 77 = 1\) inch.
  • The bookshelf will fit between the windows with \(1\) inch remaining.
  • The final answer is \(\boxed{\text{The bookshelf will fit between the windows with 1 inch remaining.}}\)

Explanation

  1. Converting the Maximum Width to Inches

The bookshelf must fit into a space that is no wider than \(6 \frac{1}{2}\) feet. To compare this to the bookshelf's width of \(77\) inches, we first convert the maximum width into inches. Since there are \(12\) inches in \(1\) foot, we multiply the maximum width by \(12\):
\[6 \frac{1}{2} \text{ feet} = 6.5 \text{ feet} = 6.5 \times 12 \text{ inches}\]
Performing this calculation:
\[6 \times 12 = 72\]
\[0.5 \times 12 = 6\]
\[72 + 6 = 78 \text{ inches}\]
The maximum allowable width for the space between the windows is \(78\) inches.

  1. Comparing Widths and Finding the Difference

Now that we have both the space width and the bookshelf width in the same units (inches), we compare them. The maximum space is \(78\) inches, and the bookshelf is \(77\) inches wide. Since \(77\) is less than \(78\), the bookshelf will fit between the windows. To find the remaining room, we subtract the width of the bookshelf from the maximum allowed width:
\[78 \text{ inches} - 77 \text{ inches} = 1 \text{ inch}\]
This means the bookshelf fits with \(1\) inch of space remaining.

  1. Final Conclusion

Comparing our result with the provided options, we see that the statement "The bookshelf will fit between the windows with \(1\) inch remaining" correctly describes the relationship. Thus, the correct option is the third one.

Examples

Understanding unit conversion is essential in many everyday situations, such as home improvement projects, cooking, and traveling. For example, when buying furniture, you often need to convert dimensions between feet and inches to ensure items will fit in your home. By mastering these conversions and comparisons, you can make informed decisions and avoid common measurement errors.

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