Finding the Third Proportional to 105,414 and 231,564

Step by Step Solution

1. Step 1: Write the proportion equation
   105,414 : 231,564 = 231,564 : x
2. Step 2: Convert to fraction form
   105,414/231,564 = 231,564/x
3. Step 3: Cross multiply
   105,414x = 231,564 × 231,564
4. Step 4: Simplify right side
   105,414x = 53,621,886,096
5. Step 5: Solve for x
   x = 53,621,886,096/105,414
6. Step 6: Final answer
   x = 508,678.98