To solve the problem, we need to find the values of \( x \) and \( y \) such that the three fractions \( \frac{6}{14}, \frac{x}{7}, \frac{24}{y} \) are equivalent.
First, let's simplify the fraction \( \frac{6}{14} \):
\[ \frac{6}{14} = \frac{3}{7} \]
Now, we want to set the other fractions equal to \( \frac{3}{7} \).
- Finding \( x \):
Set \( \frac{x}{7} = \frac{3}{7} \).
To solve for \( x \): \[ x = 3 \]
- Finding \( y \):
Set \( \frac{24}{y} = \frac{3}{7} \).
Cross-multiply to solve for \( y \): \[ 3y = 24 \cdot 7 \] Calculating \( 24 \cdot 7 \): \[ 24 \cdot 7 = 168 \] So, \[ 3y = 168 \] Dividing both sides by 3 gives: \[ y = \frac{168}{3} = 56 \]
Therefore, the answers are: \[ x = 3, \quad y = 56 \]