Question

The mean of three numbers x, y and z is 6 and the mean of five numbers x, y, z, a and b is 8.

Answer 1

Answer:

11

Step-by-step explanation:

To find the mean of a set of numbers, we add all of the numbers together and divide the sum by the size of the set. For that first set, we have three numbers, x, y and z, so the equation for their mean would be

$\dfrac{x+y+z}{3}=6$

We can rearrange this equation by multiplying both sides by 3, getting the equivalent equation

$x+y+z=18\ \ \ \ (1)$

Let's do the same thing for the second mean:

$\dfrac{x+y+z+a+b}{5}=8$

$x+y+z+a+b=40\ \ \ \ (2)$

With the two equations we've obtained, we can subtract (1) from (2) to get rid of x, y, and z, leaving us with

$a+b=22$

To find the mean of a and b now, all we have to do is divide both sides of the equation by 2, and we see that

$\dfrac{a+b}{2}=11$