Finding the Third Proportional to 86,409 and 206,086.50

Step by Step Solution

1. Step 1: Write the proportion equation
   86,409 : 206,086.50 = 206,086.50 : x
2. Step 2: Convert to fraction form
   86,409/206,086.50 = 206,086.50/x
3. Step 3: Cross multiply
   86,409x = 206,086.50 × 206,086.50
4. Step 4: Simplify right side
   86,409x = 42,471,645,482.25
5. Step 5: Solve for x
   x = 42,471,645,482.25/86,409
6. Step 6: Final answer
   x = 491,518.77