Direct Variation Problem Solution
The image shows a direct variation problem where \( y \) is directly proportional to \( x \). It states that \( y = 10 \) when \( x = 14 \) and asks for the value of \( y \) when \( x = 21 \).
In such problems, the ratio \( y/x \) remains constant, so we have:
\[ \frac{y_1}{x_1} = \frac{y_2}{x_2} \]
Given \( y_1 = 10 \) and \( x_1 = 14 \), we can express \( y_2 \) in terms of \( x_2 = 21 \) using the direct variation formula:
\[ \frac{10}{14} = \frac{y_2}{21} \]
To find \( y_2 \), we solve:
\[ y_2 = \frac{10}{14} \times 21 \]
\[ y_2 = \frac{10 \times 21}{14} \]
Now simplify the fraction:
\[ y_2 = \frac{10 \times 3}{2} \]
\[ y_2 = \frac{30}{2} \]
\[ y_2 = 15 \]
Hence when \( x = 21 \), \( y = 15 \).
