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

B

Step-by-step explanation:

Let's convert these written languages into mathematical expressions:

"x is the average of m and 9": x =
`(m +9)/(2)`

"y is the average of 2m and 15": y =
`(2m +15)/(2)`

"z is the average of 3m and 18": z =
`(3m +18)/(2)`

Now, we want to find the value of the average of x, y, and z in terms of m. The average of x, y, and z can be written as:
`(x+y+z)/(3)`. Let's substitute each of the expressions we have above in for x, y, and z:

`((m +9)/(2)+(2m +15)/(2)+(3m +18)/(2))/(3)=((m+9)+(2m+15)+(3m+18))/(6) =(6m+42)/(6) =m+7`

The answer is B.

Hope this helps!

Answer 2

B.) M + 7

Step-by-step 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+9/ 2 , Y = 2m+15/2 , Z = 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:

[ m+9 /2 + 2m+15/ 2 + 3m+18/2 ] / 3

This fraction can be simplified to m+7.