If x is the average, the 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?
Solution:
â€‹Since the average (arithmetic mean) of 2 numbers is equal to the sum of the 2 numbers divided by 2, the equations
\[ x = \frac{m + 9}{2}, y = \frac{2m + 15}{2}, z = \frac{3m + 18}{2}\]
are true. The average of x, y, and z is given by (x+y+z)/3. Substituting the expressions in m for each variable (x, y, z) gives
\[ \frac{\frac{m + 9}{2} + \frac{2m + 15}{2} + \frac{3m + 18}{2}}{3}\]
This fraction can be simplified to m+7.
The final answer is B.
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