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Algebra / Linear equations in one variable Difficulty: Hard

A manufacturing plant makes $10$ -inch, $9$ -inch, and $7$ -inch frying pans. During a certain day, the number of $10$ -inch frying pans that the manufacturing plant makes is $4$ times the number $n$ of $9$ -inch frying pans it makes, and the number of $7$ -inch frying pans it makes is $10$ . During this day, the manufacturing plant makes $100$ frying pans total. Which equation represents this situation?

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Explanation

Choice D is correct. It's given that during a certain day, the number of $9$ -inch frying pans the manufacturing plant makes is $n$ and the number of $7$ -inch frying pans it makes is $10$ . It's also given that during this day the number of $10$ -inch frying pans that the manufacturing plant makes is $4$ times the number of $9$ -inch frying pans, or $4 n$ . Therefore, the total number of $7$ -inch, $9$ -inch, and $10$ -inch frying pans the manufacturing plant makes is $n + 10 + 4 n$ , or $5 n plus 10$ . It's given that during this day the manufacturing plant makes $100$ frying pans total. Thus, the equation $5 n + 10 = 100$ represents this situation.

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

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

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