Nice question!
Given: The arithmetic mean of 3, 6, 9, a, b is 6.2

We can write: \(\frac{3+6+9+a+b}{5} = 6.2\)

Multiply both sides of the equation by 5 to get: \(3+6+9+a+b = 31\)

Simplify: \(18+a+b = 31\)

Subtract \(18\) from both sides: Simplify: \(a+b = 13\)

We have:
QUANTITY A: 6 - a
QUANTITY B: b - 6

Let's apply some matching operations (my favorite technique! See video below for more information)

Add 6 to both quantities to get:
QUANTITY A: 12 - a
QUANTITY B: b

Add a to both quantities to get:
QUANTITY A: 12
QUANTITY B: a + b

Since we already learned that \(a+b = 13\), we can substitute to get:
QUANTITY A: 12
QUANTITY B: 13

Answer: B

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