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.

Find the mean of a and b.
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Answer 1

11

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

`(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:

`(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

`(a+b)/(2)=11`