Answer :
To find the value of [tex]\( x \)[/tex], we need to understand that the mean (average) of a set of numbers is found by adding all the numbers together and then dividing by the total number of values.
In this problem, we have four numbers: 31.7, 42.8, 26.4, and [tex]\( x \)[/tex]. We are told that the mean of these numbers is 35.
Let's go through the steps:
1. Understand the Mean Formula:
[tex]\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\][/tex]
2. Set Up the Equation:
Given that the mean is 35 and there are 4 numbers, we can write the equation:
[tex]\[
\frac{31.7 + 42.8 + 26.4 + x}{4} = 35
\][/tex]
3. Solve for the Total Sum:
Multiply both sides by 4 to eliminate the fraction:
[tex]\[
31.7 + 42.8 + 26.4 + x = 35 \times 4
\][/tex]
4. Calculate the Right Side:
[tex]\[
35 \times 4 = 140
\][/tex]
5. Find the Current Sum:
Now, add up the numbers you already have:
[tex]\[
31.7 + 42.8 + 26.4 = 100.9
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
Subtract the current sum from the total sum:
[tex]\[
x = 140 - 100.9
\][/tex]
[tex]\[
x = 39.1
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 39.1. The correct option is A. 39.1.
In this problem, we have four numbers: 31.7, 42.8, 26.4, and [tex]\( x \)[/tex]. We are told that the mean of these numbers is 35.
Let's go through the steps:
1. Understand the Mean Formula:
[tex]\[
\text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of values}}
\][/tex]
2. Set Up the Equation:
Given that the mean is 35 and there are 4 numbers, we can write the equation:
[tex]\[
\frac{31.7 + 42.8 + 26.4 + x}{4} = 35
\][/tex]
3. Solve for the Total Sum:
Multiply both sides by 4 to eliminate the fraction:
[tex]\[
31.7 + 42.8 + 26.4 + x = 35 \times 4
\][/tex]
4. Calculate the Right Side:
[tex]\[
35 \times 4 = 140
\][/tex]
5. Find the Current Sum:
Now, add up the numbers you already have:
[tex]\[
31.7 + 42.8 + 26.4 = 100.9
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
Subtract the current sum from the total sum:
[tex]\[
x = 140 - 100.9
\][/tex]
[tex]\[
x = 39.1
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 39.1. The correct option is A. 39.1.
