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If y = 2x + 1, what is the arithmetic mean of 2x, 2x, y, and 3y, in terms of x?

  1. 2x
  2. 2x + 1
  3. 3x + 1
  4. None of the above
Explanation

Answer: C - Where y = 2x +1, the arithmetic mean of 2x, 2x, y, and 3y is 3x + 1.

The arithmetic mean (average) is equal to the sum of the items divided by the number of items.

Average = (2x + 2x + y + 3y) ÷ 4 = (4x + 4y) ÷ 4 = x + y

Substituting 2x + 1 for y: x + (2x + 1) = 3x + 1

Check (assume x = 3): (2(3) + 2(3) + 7 + 3(7)) ÷ 4 = (6 + 6 + 7 + 21) ÷ 4 = 40 ÷ 4 = 10 = 3(3) + 1

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