Manipulating Averages

Question

If you have multiple numbers and you want to manipulate their combined average with the next number, what's the formula? Example with 3 numbers:

21, 5, 4, $x$

Current average $= 10= \frac{(21+5+4)}3$

If, for example, you want to manipulate the average to be 7 with the 4th number, then $x = $?

Answer 1

$$\text{Average} = \frac{\text{Sum of elements}}{\text{Number of elements}}$$

If you want to manipulate the average simply include your new value: $$7 = \frac{21+5+4+x}{4}$$ $$28 = 30+x$$ $$x = -2$$