Question

The average of `x` and `y` is `5` and the average `x, y,` and `z` is `8`. What is the value of `z`?

Answer 1

`z=14`

Explanation:

The average of a set of values is given by:

`m = sum_i^N x_i/N`

Where the `x_i`'s are the individual values, and there are `N` such values. Of course, this is much easier to see for the specific example of our question where we have for the first average:

`m_1=5=(x+y)/2`

the second average contains three values:

`m_2 = 8 = (x+y+z)/3`

If we take the equation for the first average, we can multiply both sides by 2 to obtain:

`x+y=10`

which we can then substitute into the equation for the second average:

`8=(10+z)/3`

which can be solved for `z` giving

`z=14`