To make the fractions \( \frac{614}{1} \), \( \frac{x}{7} \), and \( \frac{24}{y} \) equivalent, we can set up the following equations based on the property of equivalent fractions:
- \( \frac{614}{1} = \frac{x}{7} \)
- \( \frac{614}{1} = \frac{24}{y} \)
Step 1: Solve for \( x \)
Using the first equation: \[ 614 = \frac{x}{7} \]
Multiply both sides by 7: \[ x = 614 \times 7 \]
Calculating \( x \): \[ x = 614 \times 7 = 4298 \]
Step 2: Solve for \( y \)
Using the second equation: \[ 614 = \frac{24}{y} \]
Cross-multiply: \[ 614y = 24 \]
Now, divide both sides by 614: \[ y = \frac{24}{614} \]
Since this fraction can be simplified, we can reduce it: \[ y = \frac{12}{307} \]
So the values of \( x \) and \( y \) that make the three fractions equivalent are: \[ x = 4298, \quad y = \frac{12}{307} \]
You can leave \( y \) as \( \frac{12}{307} \) or continue simplifying it in numerical form, but for clarity, we will keep it in fractional form.
Final Answer: \[ x = 4298, \quad y = \frac{12}{307} \]