Finding the Third Proportional to 321,665 and 686,078

Step by Step Solution

1. Step 1: Write the proportion equation
   321,665 : 686,078 = 686,078 : x
2. Step 2: Convert to fraction form
   321,665/686,078 = 686,078/x
3. Step 3: Cross multiply
   321,665x = 686,078 × 686,078
4. Step 4: Simplify right side
   321,665x = 470,703,022,084
5. Step 5: Solve for x
   x = 470,703,022,084/321,665
6. Step 6: Final answer
   x = 1,463,333.04