Finding the Third Proportional to 82,106 and 177,705.50

Step by Step Solution

1. Step 1: Write the proportion equation
   82,106 : 177,705.50 = 177,705.50 : x
2. Step 2: Convert to fraction form
   82,106/177,705.50 = 177,705.50/x
3. Step 3: Cross multiply
   82,106x = 177,705.50 × 177,705.50
4. Step 4: Simplify right side
   82,106x = 31,579,244,730.25
5. Step 5: Solve for x
   x = 31,579,244,730.25/82,106
6. Step 6: Final answer
   x = 384,615.55