Direct Variation Problem Solution
The image features a mathematical problem that reads: "Given \( x \) and \( y \) = 65 when \( x = 5 \), find \( y \) when \( x = 2 \)."
This problem describes a direct variation between \( x \) and \( y \), where their product is constant. Initially, when \( x = 5 \), \( y \) is such that \( x \cdot y = 65 \).
First, we can find the initial value of \( y \) when \( x = 5 \):
\[ 5 \cdot y = 65 \]
\[ y = 65 / 5 \]
\[ y = 13 \]
Now that we know the relationship between \( x \) and \( y \) is such that their product is always 65, we can use this information to find \( y \) when \( x = 2 \):
\[ x \cdot y = 65 \]
\[ 2 \cdot y = 65 \]
\[ y = 65 / 2 \]
\[ y = 32.5 \]
Therefore, when \( x = 2 \), \( y \) is 32.5.
