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Choice A is correct. It’s given that the ratio of black pens to red pens is $8$ to $1$. Therefore, there are $\frac{1}{8}$ as many red pens as black pens in the box. It’s also given that there are $40$ black pens in the box. Therefore, the number of red pens is $\frac{1}{8}$ of the $40$ black pens. Thus, the number of red pens is $40\left(\frac{1}{8}\right)$, or $5$.

Choice B is incorrect. This is the number of black pens in the box for every red pen.

Choice C is incorrect. This is the number of black pens in the box.

Choice D is incorrect. This is the number of red pens in the box if the ratio of black pens to red pens is $1$ to $8$.