[Video] Q29: If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m ?

Explanation for Question 29 From the Math (Calc) Section on the Official Sat Practice Test 4

So now looking at question number 29, 2 which says that if X is the average arithmetic mean, 3 right. So essentially we're just talking about averages here of M and nine, 4 right? So X is the average of M and nine. 5 And why is the average of two times N plus 15 and Z is 6 the average of three M and 18. 7 What is the average of X, Y, and Z in terms of them? 8 Okay. So there's a lot happening here, but first thing we need to do 9 is figure out what is X, 10 what is Y um, and what is Z? 11 Right? So X is the average of M and nine. 12 So X is really equal to M plus nine divided by two, 13 right? Because we have two numbers, M and nine, 14 then we're going to divide those by two. And then we're told that Y 15 right, is the average of two M in 15. 16 So that's two M plus 15. Again, we still only have two numbers, 17 even though M is being divided by two, it's still really only two numbers 18 because these are being multiplied. Um, 19 and then finally, Z we'll do the same thing, 3m plus 18 divided by 20 two. So we have these three numbers now in terms of M right, 21 we don't have an actual number, just an expression. 22 Um, and now we need to find the average of the three of these 23 together. So what we need to do is M plus nine, 24 over two X plus two N plus 15, 25 over two, which is why. So now we've added X to Y. 26 And then finally, you know, we'll add Z, which was three M plus 18, 27 over two, and all of these have a common denominator. 28 Um, but actually before we get there...