Question

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?

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

Answer 1

ANSWER EXPLANATION: Since the average (arithmetic mean) of two numbers is equal to the sum of the two numbers divided by 2, the equations x=m+92, y=2m+152, z=3m+182are true. The average of x, y, and z is given by x+y+z3. Substituting the expressions in m for each variable (x, y, z) gives

[m+92+2m+152+3m+182]3

This fraction can be simplified to m+7.

The final answer is B.

Answer 2

m+9/2=x

2m+15/2=y

3m+18/2=7

Now,

x+y+7/3

=(m+9/2)+(2m+15/2)+(3m+18/2)/3

=m+9+2m+15+3m+18/2/3

=6m+42/6

=6(m+7)/6

=m+7

Hence, the answer is B)m+7.

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