Finding the Third Proportional to 509.73 and 650.69

Step by Step Solution

1. Step 1: Write the proportion equation
   509.73 : 650.69 = 650.69 : x
2. Step 2: Convert to fraction form
   509.73/650.69 = 650.69/x
3. Step 3: Cross multiply
   509.73x = 650.69 × 650.69
4. Step 4: Simplify right side
   509.73x = 423,396.76
5. Step 5: Solve for x
   x = 423,396.76/509.73
6. Step 6: Final answer
   x = 830.63