Finding the Third Proportional to 177,102 and 382,189.50

Step by Step Solution

1. Step 1: Write the proportion equation
   177,102 : 382,189.50 = 382,189.50 : x
2. Step 2: Convert to fraction form
   177,102/382,189.50 = 382,189.50/x
3. Step 3: Cross multiply
   177,102x = 382,189.50 × 382,189.50
4. Step 4: Simplify right side
   177,102x = 146,068,813,910.25
5. Step 5: Solve for x
   x = 146,068,813,910.25/177,102
6. Step 6: Final answer
   x = 824,772.24