Question

Write and solve an equation to find the value of the variable.

104, 137, 154, 131, x ; mean = 130



127


124


122


125

Answer 1

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**.