Question

1.
Write and solve an equation to find the value of the variable.

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

Answer 1

To find the value of \( x \) given the mean of the numbers \( 104, 137, 154, 131, x \) is 130, we can set up the equation based on the definition of the mean.

The mean is calculated as the sum of all values divided by the number of values:

\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}
\]

In this case, the number of values is 5 (the four given numbers plus \( x \)). Therefore, the equation for the mean is:

\[
130 = \frac{104 + 137 + 154 + 131 + x}{5}
\]

Now, let's calculate the sum of the known values:

\[
104 + 137 + 154 + 131 = 526
\]

Now substituting that back into the equation:

\[
130 = \frac{526 + x}{5}
\]

Next, we multiply both sides of the equation by 5 to eliminate the fraction:

\[
130 \cdot 5 = 526 + x
\]

\[
650 = 526 + x
\]

Now, we isolate \( x \):

\[
x = 650 - 526
\]

\[
x = 124
\]

Thus, the value of \( x \) is \( \boxed{124} \).