# M:C:MC:8

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A company’s manager estimated that the cost *C*, in dollars, of producing *n* items is . The company sells each item for $12. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of *n* for which the manager estimates that the company will make a profit?

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Choice C is correct. One method to find the correct answer is to create an inequality. The income from sales of *n* items is 12*n.* For the company to profit, 12*n* must be greater than the cost of producing *n* items; therefore, the inequality can be used to model the context. Solving this inequality yields

Choice A is not the correct answer. This answer may result from a misunderstanding of the properties of inequalities. The student may have found the number of items of the break-even point as 70 and used the incorrect notation to express the answer, or the student may have incorrectly modeled the scenario when setting up an inequality to solve.

Choice B is not the correct answer. This answer may result from a misunderstanding of how the cost equation models the scenario. A student who uses the cost of $12 as the number of items *n* and evaluates the expression 7*n* will find the value of 84. A student who does not understand how the inequality relates to the scenario may think *n* should be less than this value.

Choice D is not the correct answer. This answer may result from a misunderstanding of how the cost equation models the scenario. A student who uses the cost of $12 as the number of items *n* and evaluates the expression 7*n* will find the value of 84. A student who does not understand how the inequality relates to the scenario may think *n* should be greater than this value.

Students must interpret an expression or equation that models a real-world situation and be able to interpret the whole expression (or specific parts) in terms of its context.