Finding the Third Proportional to 261,380 and 384,414

Step by Step Solution

1. Step 1: Write the proportion equation
   261,380 : 384,414 = 384,414 : x
2. Step 2: Convert to fraction form
   261,380/384,414 = 384,414/x
3. Step 3: Cross multiply
   261,380x = 384,414 × 384,414
4. Step 4: Simplify right side
   261,380x = 147,774,123,396
5. Step 5: Solve for x
   x = 147,774,123,396/261,380
6. Step 6: Final answer
   x = 565,361.25