Roberto is an insurance agent who sells two types of policies: a $50,000 policy and a $100,000 policy. Last month, his goal was to sell at least 57 insurance policies. While he did not meet his goal, the total value of the policies he sold was over $3,000,000. Which of the following systems of inequalities describes x, the possible number of $50,000 policies, and y, the possible number of $100,000 policies, that Roberto sold last month?
Correct answer: C. x + y < 5750,000 x + 100,000 y > 3,000,000
- A. x + y < 5750,000 x + 100,000 y < 3,000,000
- B. x + y > 5750,000 x + 100,000 y > 3,000,000
- C. x + y < 5750,000 x + 100,000 y > 3,000,000
- D. x + y > 5750,000 x + 100,000 y < 3,000,000
Explanation
Choice C is correct. Since Roberto sells only two types of policies and he didn't meet his goal of selling at least 57 policies, the sum of x, the number of $50,000 policies, and y, the number of $100,000 policies, must be less than 57. Symbolically, that is x + y < 57. The total value, in dollars, from selling x number of $50,000 policies is 50,000x. The total value, in dollars, from selling y number of $100,000 policies is 100,000y. Since the total value of the policies he sold was over $3,000,000, it follows that 50,000x + 100,000y > 3,000,000. Only choice C has both correct inequalities.
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