To solve the problem, we need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 12 \)[/tex], given that [tex]\( x \)[/tex] is inversely proportional to [tex]\( y \)[/tex].
When two quantities are inversely proportional to each other, their product is a constant. Mathematically, this relationship is described as:
[tex]\[ x \cdot y = k \][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality.
We are given that:
[tex]\[ x = 60 \quad \text{and} \quad y = 0.5 \][/tex]
First, we determine the constant of proportionality, [tex]\( k \)[/tex], using the given values:
[tex]\[ k = x \cdot y = 60 \cdot 0.5 \][/tex]
[tex]\[ k = 30 \][/tex]
Now, we need to find [tex]\( x \)[/tex] when [tex]\( y = 12 \)[/tex]. Using the constant of proportionality, we set up the equation:
[tex]\[ x \cdot y = k \][/tex]
[tex]\[ x \cdot 12 = 30 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{30}{12} \][/tex]
[tex]\[ x = 2.5 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 12 \)[/tex] is [tex]\( 2.5 \)[/tex], or option B.
Thus, the best answer is:
B. 2.5
