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M:C:MC:8

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A company’s manager estimated that the cost C, in dollars, of producing n items is C equals 7 n plus 350. 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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n less than 70

Correct Answer: 
No

n less than 84

Correct Answer: 
No

n greater than 70

Correct Answer: 
Yes

n greater than 84

Correct Answer: 
No

View Correct Answer

Choice C is correct. One method to find the correct answer is to create an inequality. The income from sales of n items is 12n. For the company to profit, 12n must be greater than the cost of producing n items; therefore, the inequality 12 n greater than 7 n plus 350 can be used to model the context. Solving this inequality yields n greater than 70.

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 7n 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 7n 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.

Question Difficulty: 
medium
Objective: 

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.