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Algebra / Linear equations in one variable Difficulty: Hard

A factory makes $9$ -inch, $7$ -inch, and $4$ -inch concrete screws. During a certain day, the number of $9$ -inch concrete screws that the factory makes is $5$ times the number $n$ of $7$ -inch concrete screws, and the number of $4$ -inch concrete screws is $22$ . During this day, the factory makes $100$ concrete screws total. Which equation represents this situation?

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Explanation

Choice D is correct. It's given that during a certain day at a factory, the number of $7$ -inch concrete screws the factory makes is $n$ and the number of $4$ -inch concrete screws the factory makes is $22$ . It's also given that during this day the number of $9$ -inch concrete screws the factory makes is $5$ times the number of $7$ -inch concrete screws, or $5 n$ . Therefore, the total number of $7$ -inch, $9$ -inch, and $4$ -inch concrete screws is $n + 5 n + 22$ , or $6 n plus 22$ . It's given that during this day, the factory makes $100$ concrete screws total. Thus, the equation $6 n + 22 = 100$ represents this situation.

Choice A is incorrect. This equation represents a situation where the total length, in inches, of all the concrete screws, rather than the total number of concrete screws, is $100$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This equation represents a situation where the total number of $9$ -inch concrete screws and $4$ -inch concrete screws, not including the $7$ -inch concrete screws, is $100$ .