Question

Let x, y, and z be non-zero numbers such that the average (arithmetic mean) of x and twice y is equal to the average (arithmetic mean) of y and twice z. What is the average (arithmetic mean) of x and y?

A. z/2
B. z
C. 2z
D. z − x
E. z − y

Answer 1

Answer:

$(b) \: \: \: \\ z \: \: is \: correct.$

Step-by-step explanation:

$x > 0 \\ y > 0 \\ z > 0 \\ \\ \frac{x + 2y}{2} = \frac{y + 2z}{2} \\ \\ x + 2y = y + 2z \\ \\ x + y = 2z \\ \\ \frac{x + y}{2} = z \\ \\ therefore \: \: average \: of \: x \: and \: y \: is \: z. \\ \\ option \: (b) \: is \: correct$