8. A carpenter is installing shelves in 2 offices. Each office will have 4 shelves. The wood the carpenter wants to use comes in 6-foot-long boards. Each shelf is 2 ¼ feet long and is constructed from a single board. How many boards does the carpenter need to buy to make the shelves?
Answer: D
The carpenter needs to buy 4 boards to make the shelves.
To determine the number of boards needed, we first calculate the total length of wood required for all shelves. Each office has 4 shelves, and with 2 offices, that totals 8 shelves. Each shelf requires 2 ¼ feet of wood, leading to a total requirement of 18 feet of wood. Since each board is 6 feet long, the carpenter will need 4 boards to meet this requirement.
A) 2
This option is incorrect because purchasing only 2 boards would provide only 12 feet of wood (2 boards x 6 feet), which is insufficient for the 18 feet needed for the 8 shelves.
B) 8
Choosing 8 boards is also incorrect. While this would provide 48 feet of wood (8 boards x 6 feet), it significantly exceeds the requirement of 18 feet, resulting in unnecessary excess material.
C) 3
Option C is incorrect as well. Buying 3 boards would yield 18 feet of wood (3 boards x 6 feet), which meets the requirement. However, since each board can only be used partially and cannot be cut for multiple shelves, the actual number of full boards needed is 4.
D) 4
This option is correct. By purchasing 4 boards, the carpenter will have exactly 24 feet of wood (4 boards x 6 feet), which is sufficient to construct the 8 shelves, as each shelf requires 2 ¼ feet.
Conclusion
The correct answer is 4 boards, as this provides enough wood to meet the requirements for all shelves without falling short or excessively exceeding the needed material. Other options either do not provide enough wood or result in unnecessary surplus, demonstrating a clear understanding of the material requirements for the task at hand.