If x is the average (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 ?

Options

A. m + 6
B. m + 7
C. 2m + 14
D. 3m + 21

Answer

B

Explanation

Since the average of 2 numbers is the sum of the 2 numbers divided by 2, the equations ` x = ( m + 9 ) /(2 ) , y = ( 2m +15 ) /(2 ) and z = ( 3m + 18 ) /(2) ` are true. The average of x, y and z is given by ` ( x + y + z )/(3) `
Substituting the preceding expressions in m for each variable gives `((m + 9 ) /(2) + ( 2m + 15 ) /(2) + ( 3m + 18 )/(2 ))/(3 ) ` . This fraction can be simplified to ` ( 6m + 42 )/(6)`,
Choices A, C, and D are incorrect and may be the result of conceptual errors or calculation errors. For example, choice D is the sum of x, y, and z, not the average.