To find the value of \( x \) that makes the mean of the numbers \( 104, 137, 154, 131, x \) equal to 130, we can set up an equation.
The mean (average) is calculated as follows:
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]
In this case, the mean is given as 130, and we have 5 values (including \( x \)). Therefore, we can set up the equation:
\[ 130 = \frac{104 + 137 + 154 + 131 + x}{5} \]
Now, let's calculate the sum of the known values:
\[ 104 + 137 + 154 + 131 = 526 \]
Now substituting this sum back into the mean equation gives:
\[ 130 = \frac{526 + x}{5} \]
Next, we can multiply both sides by 5 to eliminate the fraction:
\[ 130 \times 5 = 526 + x \]
\[ 650 = 526 + x \]
Now, we can solve for \( x \) by subtracting 526 from both sides:
\[ x = 650 - 526 \]
\[ x = 124 \]
So, the value of \( x \) is 124.
To confirm, we can calculate the new mean with \( x = 124 \):
The new values are \( 104, 137, 154, 131, 124 \).
Calculating the sum:
\[ 104 + 137 + 154 + 131 + 124 = 650 \]
Now, calculating the mean:
\[ \text{Mean} = \frac{650}{5} = 130 \]
Thus, the mean holds true, confirming our solution. The final answer is:
124.