Finding the Third Proportional to 37,684 and 82,766

Step by Step Solution

1. Step 1: Write the proportion equation
   37,684 : 82,766 = 82,766 : x
2. Step 2: Convert to fraction form
   37,684/82,766 = 82,766/x
3. Step 3: Cross multiply
   37,684x = 82,766 × 82,766
4. Step 4: Simplify right side
   37,684x = 6,850,210,756
5. Step 5: Solve for x
   x = 6,850,210,756/37,684
6. Step 6: Final answer
   x = 181,780.35