Finding the Third Proportional to 205,840 and 417,404

Step by Step Solution

1. Step 1: Write the proportion equation
   205,840 : 417,404 = 417,404 : x
2. Step 2: Convert to fraction form
   205,840/417,404 = 417,404/x
3. Step 3: Cross multiply
   205,840x = 417,404 × 417,404
4. Step 4: Simplify right side
   205,840x = 174,226,099,216
5. Step 5: Solve for x
   x = 174,226,099,216/205,840
6. Step 6: Final answer
   x = 846,415.17