Finding the Third Proportional to 102,085 and 149,665.50

Step by Step Solution

1. Step 1: Write the proportion equation
   102,085 : 149,665.50 = 149,665.50 : x
2. Step 2: Convert to fraction form
   102,085/149,665.50 = 149,665.50/x
3. Step 3: Cross multiply
   102,085x = 149,665.50 × 149,665.50
4. Step 4: Simplify right side
   102,085x = 22,399,761,890.25
5. Step 5: Solve for x
   x = 22,399,761,890.25/102,085
6. Step 6: Final answer
   x = 219,422.66