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
[tex]\dfrac{x+y+z}{3}=6[/tex]
We can rearrange this equation by multiplying both sides by 3, getting the equivalent equation
[tex]x+y+z=18\ \ \ \ (1)[/tex]
Let's do the same thing for the second mean:
[tex]\dfrac{x+y+z+a+b}{5}=8[/tex]
[tex]x+y+z+a+b=40\ \ \ \ (2)[/tex]
With the two equations we've obtained, we can subtract (1) from (2) to get rid of x, y, and z, leaving us with
[tex]a+b=22[/tex]
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
[tex]\dfrac{a+b}{2}=11[/tex]
