The mean of the numbers 13, 16, x, 18, 21, 2x, 35, is 22. Find the value of x
To find the value of x, we start by understanding that the mean (or average) of a set of numbers is calculated by adding all the numbers together and then dividing by the count of the numbers.
Given the numbers: 13, 16, x, 18, 21, 2x, and 35, the mean is provided as 22. So, let's sum up all the numbers:
(13) + (16) + (x) + (18) + (21) + (2x) + (35) = Total Sum
First, combine the constant numbers:
13 + 16 + 18 + 21 + 35 = 103
Then add the terms involving x:
The expression becomes:
103 + x + 2x = Total Sum
This simplifies to:
103 + 3x = Total Sum
According to the mean formula:
Total Sum / Number of terms = Mean
We are given the mean as 22, and we have 7 numbers (since there are 7 terms):
(103 + 3x) / 7 = 22
Cross-multiply to get rid of the fraction:
103 + 3x = 22 * 7
Calculate 22 * 7:
103 + 3x = 154
Subtract 103 from both sides to solve for x:
3x = 154 - 103
3x = 51
Now, divide both sides by 3 to find x:
x = 51 / 3
x = 17
Therefore, the value of x is 17.