"Average" Averages On the SAT (Pun Totally Intended)

The average person would know how to calculate averages. (Pun Intended.) Since you would obviously know how to find the average of something, I wouldn't need to show you the average (arithmetic mean) formula. But since I am a nice guy, here you go:

WTH is this thing?

If you are freaking out at how complicated the "average formula" is– don't worry, this is just a fancy alternative for the "average formula". Here's the one we are all familiar with:

Better? Why did I show you an obscure version of the "average formula"? Because I can, and I like to mess around with stuff like this. 

Now, let's get serious.

When dealing with averages on the SAT Math, you will most likely NOT encounter a simple, "find the average of the following five terms: 5, 10, 15, 20, and 25." That's way too easy. Remember, to do well on the SAT Math, you need to know how to play around with basic math concepts. For solving SAT average problems, knowing how to manipulate the "average formula" will be paramount.

Notice how I multiplied each side of the equation by "Number of Terms" and got the formula above? You will need this to solve SAT average problems.

Try out the problem below.

The Squad

18.       Ash Ketchum has six Pokémon weighing an average of 45 pounds. He heads to the Pokémon Center, and drops off three Pokémon weighing a total of 90 pounds. He also picks up one Pokémon weighing 50 pounds. He heads to another Pokémon Center, picking up two more Pokémon, which weigh 30 and 40 pounds. What is the average weight in pounds, of the Pokémon that remain with Ash Ketchum?

(A) 45

(B) 47

(C) 50

(D) 55

(E) 60

Remember how I wrote "let's get serious"? I still stay true to that. Pokémon is just as serious as prepping for the SAT. (Sarcasm at its finest.) Obviously, the SAT won't be mentioning Pokémon in its problems. I just figured that using Pokémon would make the "average" SAT average problem less "average". If Pokémon is throwing you off (which it really shouldn't), then here's a "normal" average problem.

PWN the SAT

How to solve #18:

18.       Ash Ketchum has six Pokémon weighing an average of 45 pounds₁. He heads to the Pokémon Center, and drops off three Pokémon weighing a total of 90 pounds₂. He also picks up one Pokémon weighing 50 pounds₃. He heads to another Pokémon Center, picking up two more Pokémon, which weigh 30 and 40 pounds₄. What is the average weight in pounds, of the Pokémon that remain with Ash Ketchum?₅

(A) 45

(B) 47

(C) 50

(D) 55

(E) 60

Notice the subscripts 1, 2, 3, 4, and 5?
Those are there to indicate the chronology of the problem, i.e. the order of steps.

Step 1.

Ash has six Pokémon, and his Pokémon weigh an average of 45 pounds.

Plug in the numbers, and you will get the equation: 

45 pounds x 6 Pokémon  = 270 pounds of Pokémon 

Step 2.

Our hero drops off three Pokémon. And the total weight of the three dropped Pokémon is 90 pounds.

Since Ash initially had 270 pounds of Pokémon: 

270 pounds of Pokémon - 90 pounds of Pokémon  = 180 pounds of Pokémon 

Remember that Ash dropped off three Pokémon from his initial six, so he currently has three.

Step 3.

At the same Pokémon Center, Ash picks up a Pokémon that weighs 50 pounds. 

So: 180 pounds + 50 pounds = 230 pounds of Pokémon 

Don't forget that Ash added one more Pokémon to his team of three, which now makes four.

Step 4.

Our forever ten year old (get the reference?) continues his journey, and he stops by at another 

Pokémon Center, picking up two Pokémon that weigh 30 and 40 pounds.

Thus: 230 pounds + 30 pounds + 40 pounds = 300 pounds

Since Ash picked up two more Pokémon and added them to his team of four, he has a total of six Pokémon with him.

Step 5.

Now we use the "average formula": 

For this problem, the "sum of terms" is the total weight of Pokémon Ash Ketchum currently holds, which is 300 pounds. The "number of terms" is the number of Pokémon Ash Ketchum carries at the moment, which is 6. 

Plug in 300 in the "sum of terms" and 6 in the "number of terms", thus 300/6 = 50.

Therefore, the answer is 50 pounds. 

You can find the solution for #19 by clicking the link under the problem. It's basically the same idea, but the approach/setup is different (PWN the SAT uses tables).