[Video] Q12: 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?

Explanation for Question 12 From the Math (Calc) Section on the Official Sat Practice Test 8

So here, we're talking about Roberto, right? 2 And Roberto's an insurance agent who has a goal of selling 57 insurance policies. 3 But something that's important to note is that Roberto does not meet his goal 4 right. While he did not meet his goal. 5 And so we see that when we're asked, for which of the following describes 6 the, um, the policies that he sold last month, 7 if X is the number of possible $50,000 policies, 8 and why is the number of $100,000 policies? 9 If we add those together, he must've sold less than 57, 10 right? Because he didn't meet his goal. And his goal was to sell 57 11 policies. So we need the less than sign. 12 Right. And so that means we can eliminate B and we can then eliminate 13 D and now the next question is, what do we do with the second 14 equation here? If we look back at the sentence that I've highlighted in blue, 15 it says the value of the policies he sold was over $3 million. 16 Yeah. That's million. Okay. So he sold a lot, 17 right? And we want that value to be over $3 million. 18 So if we look at let's take a look at a 50,000 times, 19 X is going to be the amount of money that he made off of 20 the $50,000 policies. And then 100,000 times, 21 why is the amount of money that he made off of the $100,000 policies? 22 So all of that money together should be over 3000. 23 So what we want, here's not a less than sign, 24 but a greater than sign. And we see that greater than sign here in 25 answer choice C. So our best answer is going to be C.