[Video] Q24: Mr. kohl has a beaker containing n milliliters of solution to distribute to the students in his chemistry class. if he gives each student 3 milliliters of solution, he will have 5 milliliters left over. in order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. how many students are in the class?

Explanation for Question 24 From the Math (Calc) Section on the Official Sat Practice Test 3

Now for number 24, we're given a bunch of scenarios, 2 right. And we're told to solve for the numbers of students in the class. 3 So let's go ahead and call that variable S right. 4 And then we have a second variable, which is going to be N the 5 total amount of solution, um, 6 that Mr. Cole has. And so we noticed immediately, 7 right there, two variables happening here in S and an N. 8 And if we look further into our question, we'll see that we have two 9 different scenarios, right? There's a scenario where if we give three milliliters, 10 each student, we have five leftover and that's that, 11 then there's a scenario where if we give four milliliters, 12 each student, we have 21 leftover. 13 So two, two sets of info that we could use to create two. 14 So, uh, equations, two types of variables. 15 This is being set up to be a classic systems of equations problem, 16 right? 17 So let's start by making an equation from the orange information. 18 If I give three milliliters to each student, 19 then I gave out a total of three times S milliliters. 20 And if I had five left over, right, 21 the amount I gave out, plus what I have left over that is equal 22 to the total amount of solution that I had to start with. 23 And now making an equation from the blue section, 24 right? If I give four milliliters, each student that's four times S but I 25 need an additional 21 milliliters. 26 Right? So that means I'm, I've given out too much. 27 I'm trying to give out too much. So for S minus...