Question

If the average (arithmetic mean) of 2, 7, and x is 12, what is the value of x?

Answer 1

To find the value of x for which the average of 2, 7, and x is 12, we set up an equation and solve for x, finding that x equals 27.

Step-by-step explanation:

If the average (arithmetic mean) of 2, 7, and x is 12, we can set up an equation to find the value of x. The formula for the mean when adding x numbers together and dividing by x is the sum of the numbers divided by the number of terms. Here, we are adding three terms (2 + 7 + x) and dividing by 3 to get the mean of 12.

To solve for x, follow these steps:

1. 
   
3. Add the known numbers together: 2 + 7 = 9.
4. 
   
6. Since the mean is 12, write the equation (2 + 7 + x) / 3 = 12.
7. 
   
9. Multiply both sides by 3 to get 2 + 7 + x = 36.
10. 
    
12. Subtract the sum of the known numbers from 36: 36 - 9 = 27.
13. 
    
15. Therefore, x = 27.

So the value of x that makes the mean 12 is 27.

Answer 2

The three numbers are 2, 7 and x.

Ther sum is
2 + 7 + x = 9 + x

Because the arithmetic mean is 12, therefore
(9 + x)/3 = 12
9 + x = 12*3 = 36
x = 36 - 9 = 27

Answer: x = 27