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?

Rationale

The carpenter needs to buy 4 boards to make the shelves.

To determine the number of boards required, we first calculate the total length of wood needed for the shelves. Each office has 4 shelves, making a total of 8 shelves across both offices. Since each shelf is 2 ¼ feet long, the total length of wood required is 18 feet, which can be accommodated by 4 boards of 6 feet each.

A (2) YOUR ANSWER

Choosing 2 boards would provide only 12 feet of wood (2 boards x 6 feet), which is insufficient for the 18 feet needed for 8 shelves. This option cannot meet the total length requirement.

B (8) YOUR ANSWER

Buying 8 boards would result in 48 feet of wood (8 boards x 6 feet), which far exceeds the 18 feet needed. While this option would certainly provide enough wood, it is unnecessarily excessive and not the most efficient choice.

C (3) YOUR ANSWER

Three boards would yield 18 feet of wood (3 boards x 6 feet), which matches the total length required for the shelves. However, since only whole boards can be used and each shelf requires a single board, this option does not cover the exact number of shelves needed.

D (4) CORRECT

Four boards provide exactly 24 feet of wood (4 boards x 6 feet), which is more than sufficient for the 18 feet required for the 8 shelves. This is the correct and efficient choice for the carpenter.

Conclusion

To successfully build 8 shelves at 2 ¼ feet each, the carpenter requires a total of 18 feet of wood. By purchasing 4 boards, the carpenter not only has enough material but also adheres to the requirement that each shelf is constructed from a single board. Thus, the optimal number of boards to buy is 4.

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?

The carpenter needs to buy 4 boards to make the shelves.

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