There are three numbers: 4, 26 and 18. A fourth number creates a group average of 12. What is this fourth number?0381214

1. ### Break Down the Problem

To find the fourth number that creates an average of 12 with the numbers 4, 26, and 18, we first need to determine the total of all four numbers based on the desired average.

2. ### Relevant Concepts

The formula for the average $A$ of $n$ numbers is given by: $A = \frac{{\text{Sum of all numbers}}}{n}$ In this case, we want the average $A = 12$ for 4 numbers (the three given numbers and the unknown fourth number).

3. ### Analysis and Detail

1. Let the fourth number be $x$.
2. The sum of the first three numbers is: $4 + 26 + 18 = 48$
3. The sum of all four numbers should be: $12 \times 4 = 48$
4. Thus, we can set up the equation: $48 + x = 48$
5. To solve for $x$, we subtract 48 from both sides: $x = 48 - 48 = 0$

4. ### Verify and Summarize

We verify by adding 0 to the other numbers: $4 + 26 + 18 + 0 = 48$ The average of these four numbers is: $\frac{48}{4} = 12$ This confirms that our calculation is correct.

Final Answer

The fourth number is $0$.