Finding the Third Proportional to 82,083 and 178,543.50

Step by Step Solution

1. Step 1: Write the proportion equation
   82,083 : 178,543.50 = 178,543.50 : x
2. Step 2: Convert to fraction form
   82,083/178,543.50 = 178,543.50/x
3. Step 3: Cross multiply
   82,083x = 178,543.50 × 178,543.50
4. Step 4: Simplify right side
   82,083x = 31,877,781,392.25
5. Step 5: Solve for x
   x = 31,877,781,392.25/82,083
6. Step 6: Final answer
   x = 388,360.34