To solve this problem, we need to understand the concept of direct variation. When [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we can express this relationship with the equation:
[tex]\[ y = k \cdot x \][/tex]
where [tex]\( k \)[/tex] is the constant of variation.
We are given that [tex]\( y = 25 \)[/tex] when [tex]\( x = 140 \)[/tex]. First, we need to determine the constant [tex]\( k \)[/tex]. We do this by substituting the given values of [tex]\( y \)[/tex] and [tex]\( x \)[/tex] into the direct variation formula:
[tex]\[ 25 = k \cdot 140 \][/tex]
Solving for [tex]\( k \)[/tex], we get:
[tex]\[ k = \frac{25}{140} \][/tex]
Next, we are given [tex]\( y = 36 \)[/tex] and need to find the corresponding value of [tex]\( x \)[/tex]. We use the same direct variation formula [tex]\( y = k \cdot x \)[/tex], but this time, we substitute the known values of [tex]\( y \)[/tex] and [tex]\( k \)[/tex]:
[tex]\[ 36 = \left( \frac{25}{140} \right) \cdot x \][/tex]
To find [tex]\( x \)[/tex], we solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{36}{\frac{25}{140}} \][/tex]
Simplifying this, we get:
[tex]\[ x = 36 \cdot \frac{140}{25} \][/tex]
[tex]\[ x = 36 \cdot 5.6 \][/tex]
[tex]\[ x = 201.6 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 36 \)[/tex] is [tex]\( 201.6 \)[/tex].
Thus, the correct answer is [tex]\( \boxed{201.6} \)[/tex].
