To determine the value of \( x \) when \( y = 36 \) under the assumption that \( y \) and \( x \) have a proportional relationship, we can use the formula:
\[ \frac{y_1}{x_1} = \frac{y_2}{x_2} \]
From the problem, we know:
- \( y_1 = 24 \), \( x_1 = 16 \)
- \( y_2 = 36 \), \( x_2 = ? \)
Setting up the proportion:
\[ \frac{24}{16} = \frac{36}{x_2} \]
Cross-multiplying gives us:
\[ 24 \cdot x_2 = 16 \cdot 36 \]
Now, calculate \( 16 \cdot 36 \):
\[ 16 \cdot 36 = 576 \]
Substituting back, we have:
\[ 24 \cdot x_2 = 576 \]
Now, divide both sides by 24 to solve for \( x_2 \):
\[ x_2 = \frac{576}{24} = 24 \]
Therefore, the value of \( x \) when \( y = 36 \) is \( x = 24 \).
The correct response is:
x = 24