Final answer:
The builder needs to buy 8 packages of boards to have the required thirty-eight boards since the packages contain five boards each, and he cannot purchase a fraction of a package.
Step-by-step explanation:
The builder needs to purchase boards that come in packs of five. To find out how many packages the builder needs to buy to have at least thirty-eight boards, we perform the following calculation:
Divide the total number of boards needed by the number of boards in each package. This gives us 38 ÷ 5 = 7.6.
Since the builder cannot purchase a fraction of a package, he must round up to the nearest whole number. Therefore, the builder needs to buy 8 packages to get at least thirty-eight boards.
In summary, the builder needs to buy 8 packages of boards to ensure he has enough for his project.