The mean of four numbers is 10. If three of the numbers are 7, 8, and 11, what is the fourth number?

14, I'd imagine.

in this problem, you have 4 numbers which have to add up to be 40........ because when you divide that by 4, you get 10.

Why the hell would I do a child's homework?

The average number is 10 so 2 numbers must be a number of less than 10 and 2 must be the same number but of more than 10

from 7 and 8 you are 5 away from 10
from 11 you are 1 away from 10
therefore the missing number must be 14 because 4 + 1 = 5 away from 10

(7 + 8 + 11 + x)/4 = 10
26 + x = 40
x= 14

If X is the 4 th number , then arithmatic mean number of these 4 numbers of 7, 8 , 11 and X can be equated as ; 7 + 8 + 11 + X / 4 = 10 , then by simplifying 26 + X = 40 , So , X = 40 - 16 = 14 , therefore the 4 th number is 14 , putting the value of X = 14 in the above equation we get LHS in the equation :(7 + 8 + 11 + 14) / 4 = 40 / 4 = 10 as mean average which tallies with RHS of the equation .

show all work? such trivial problem can be solved by inspection.
if you can't multiply 10 by 4, then subtract (8+7) and 11 from it in your head to get 14, you need to restudy fundamental arithmetic

7 + 8 + 11 + x = 40

= 26 + x = 40

x = 40-26

x = 14

x = 14.

(7 + 8 + 11 + x)/4 = 10. Therefore x = (4)(10) - (7 + 8 + 11) = 40 - 26 = 14. End of story.

You have :
-----------------

xbar = ( x1 + x2 + x3 + x4 ) / ( 4 )

( 4 ) ( xbar ) - x1 - x2 - x3 = x4

x4 = ( 4 ) ( 10 ) - 7 - 8 - 11 )

x4 = 40 - 7 - 8 - 11 = 40 - 26 = 14 <--------------

(7+8+11+x)/4=10
Multiply both sides by 4
7+8+11+x=10*4
Subtract 7+8+11 from both sides
x=10*4-(7+8+11)
Simplify
x=14

Let the fourth number is 'x'
then( 7+8+11+x)/4 = 10
7+8+11+x = 10*4
7+8+11+x = 40
x = 40-7-8-11
x = 14

7+8+11+x=10*4
x=40-26
=14

For 7, 8, and 11 the differences from the mean, 10, are -3, -2 and +1 total -4.
So the difference for the last number = +4
10+4 = 14.

(7 + 8 + 11 + N)/4 = 10
7 + 8 + 11 + N = 40
N + 26 = 40
N = 14

10 × 4 - (7 + 8 + 11)
= 40 - 26
= 14
The fourth number is 14.

Mean of 4 numbers = 10 means sum of those numbers = 10 x 4
Let the no. to be found be x

7 + 8 + 11 + x = 40
= 26 + x = 40
x = 40-26
x = 14

sum of the numbers mean addition in math operation.
7+8+11+x=10
X= 10-26
X= -16