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Problem-Solving and Data Analysis / Ratios, rates, proportional relationships, and units Difficulty: Easy

In a box of pens, the ratio of black pens to red pens is $8$ to $1$ . There are $40$ black pens in the box. How many red pens are in the box?

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Explanation

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 $40 left parenthesis one eighth right parenthesis$ , 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 $8$ .