Finding the Third Proportional to 205,365 and 413,782.50

Step by Step Solution

1. Step 1: Write the proportion equation
   205,365 : 413,782.50 = 413,782.50 : x
2. Step 2: Convert to fraction form
   205,365/413,782.50 = 413,782.50/x
3. Step 3: Cross multiply
   205,365x = 413,782.50 × 413,782.50
4. Step 4: Simplify right side
   205,365x = 171,215,957,306.25
5. Step 5: Solve for x
   x = 171,215,957,306.25/205,365
6. Step 6: Final answer
   x = 833,715.37