Finding the Third Proportional to 85,578 and 206,164

Step by Step Solution

1. Step 1: Write the proportion equation
   85,578 : 206,164 = 206,164 : x
2. Step 2: Convert to fraction form
   85,578/206,164 = 206,164/x
3. Step 3: Cross multiply
   85,578x = 206,164 × 206,164
4. Step 4: Simplify right side
   85,578x = 42,503,594,896
5. Step 5: Solve for x
   x = 42,503,594,896/85,578
6. Step 6: Final answer
   x = 496,664.97