I'll give brainliest! 20 points!
i add x into the following set {9, 18, 27, 30} to make the mean of the new set equal to its median. what is the sum of all the possible values of x?

  78

Step-by-step explanation:

The mean is the sum of the 5 numbers, divided by 5:

  µ = (9 + 18 + 27 + 30 + x)/5 = (84 +x)/5 = 16.8 +x/5

The median of a 5-number set will be the middle number. Depending on the value of x, the mean/median may be 18, x, or 27, so we have three possible equations for x.

  16.8 +x/5 = 18

  x/5 = 1.2 . . . . . subtract 16.8

  x = 6 . . . . . . . . multiply by 5

___

  16.8 +x/5 = x

  16.8 = 4/5x . . . . subtract x/5

  21 = x . . . . . . . . . multiply by 5/4

___

  16.8 +x/5 = 27

  x/5 = 10.2 . . . . . . subtract 16.8

  x = 51 . . . . . . . . . . multiply by 5

___

The sum of the possible values of x is ...

  sum = 6 + 21 + 51 = 78