If the mean of the four numbers 4, 8, x, and 12 is 10, what is the value of x?

• A. 12
• B. 14
• C. 16
• D. 18

Answer: (C)

To determine the value of ( x ) when the mean of the numbers 4, 8, ( x ), and 12 equals 10, we start by using the formula for the mean, which is the sum of the numbers divided by the total count of numbers. In this case, there are four numbers, and we can set up the equation as follows:

[

\text{Mean} = \frac{4 + 8 + x + 12}{4}

]

Given that the mean is 10, we can set the equation equal to 10:

[

\frac{4 + 8 + x + 12}{4} = 10

]

Next, we simplify the left side of the equation:

[

\frac{24 + x}{4} = 10

]

Now, we eliminate the fraction by multiplying both sides by 4:

[

24 + x = 40

]

To solve for ( x ), we subtract 24 from both sides:

[

x = 40 - 24

]

[

x = 16

]

Thus, the value of ( x ) is 16. When checking this against the mean