Explanation for Question 31 From the Math (Calc) Section on the Official Sat Practice Test 3
Not for question number 31. We're told that tickets for a talent show cost 2 $2 for students and $3 for adults. 3 And Chris spent, um, at least $11, 4 but no more than $14. Right? So the amount that Chris spent was greater 5 than, or equal to 11, but less than, 6 or equal to 14, um, 7 on X student tickets and one adult ticket, 8 right? So what is one possible value of X? 9 And so what we can do here is we can see right how much 10 he spent, which is going to be 11, um, 11 not 11, right? But X number of student tickets and students were $2. 12 So it's two times X plus one adult ticket. 13 So two times X plus three, 14 right? That's the expression that shows us what Chris spent based on his tickets. 15 And so we can take that two X plus three, 16 and we can send, set that equal to the bottom amount that he spent 17 at least $11. 18 And if we subtract three here, we'll see that two X is equal to 19 eight and we can divide by two. 20 And so we can see the X is equal to four. So one possible 21 value of X then is X is equal to four. And that's what X 22 would be. Um, if he had only bought $11 worth of tickets, 23 but if you spent $14, we would take the two X plus three and 24 we could set that equal to 14. You subtract three from both sides. 25 We get two X is equal to 11, right? 26 We divided by two, we divide by two and we know 11 divided by 27 two is 5.5, right? But you can't buy half of a ticket. 28 Um, so that shows us that another possible value we would have to round 29 dow...