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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?

SAT · Math · previous-year question

  1. A.$x+y<57$ $50,000 x+100,000 y<3,000,000$
  2. B.$x+y>57$ $50,000 x+100,000 y>3,000,000$
  3. C.$x+y<57$ $50,000 x+100,000 y>3,000,000$correct
  4. D.$x+y>57$ $50,000 x+100,000 y<3,000,000$

Answer

C. $x+y<57$ $50,000 x+100,000 y>3,000,000$

Explanation

Choice $\mathbf{C}$ 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 $50,000 x$. The total value, in dollars, from selling $y$ number of $\$ 100,000$ policies is $100,000 y$. Since the total value of the policies he sold was over $\$ 3,000,000$, it follows that $50,000 x+100,000 y>3,000,000$. Onl

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