The mean of 8, 12, 16, and x is 14. Find the value of x.

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Question: The mean of 8, 12, 16, and x is 14. Find the value of x.

Options:

Correct Answer: 10

Solution:

Mean = (8 + 12 + 16 + x) / 4 = 14. Therefore, 36 + x = 56, so x = 20.

The mean of 8, 12, 16, and x is 14. Find the value of x.

The mean of 8, 12, 16, and x is 14. Find the value of x.

Step 1: Write down the numbers we have: 8, 12, 16, and x.
Step 2: Understand that the mean (average) is found by adding all the numbers together and then dividing by how many numbers there are.
Step 3: Since we have 4 numbers (8, 12, 16, and x), we will divide the total by 4.
Step 4: Set up the equation for the mean: (8 + 12 + 16 + x) / 4 = 14.
Step 5: Calculate the sum of the known numbers: 8 + 12 + 16 = 36.
Step 6: Substitute the sum back into the equation: (36 + x) / 4 = 14.
Step 7: To eliminate the division, multiply both sides of the equation by 4: 36 + x = 14 * 4.
Step 8: Calculate 14 * 4, which equals 56: 36 + x = 56.
Step 9: To find x, subtract 36 from both sides: x = 56 - 36.
Step 10: Calculate 56 - 36, which equals 20: x = 20.

Mean Calculation – Understanding how to calculate the mean (average) of a set of numbers.
Algebraic Manipulation – Solving for an unknown variable in an equation.