Finding the Third Proportional to 37,856 and 82,345

Step by Step Solution

1. Step 1: Write the proportion equation
   37,856 : 82,345 = 82,345 : x
2. Step 2: Convert to fraction form
   37,856/82,345 = 82,345/x
3. Step 3: Cross multiply
   37,856x = 82,345 × 82,345
4. Step 4: Simplify right side
   37,856x = 6,780,699,025
5. Step 5: Solve for x
   x = 6,780,699,025/37,856
6. Step 6: Final answer
   x = 179,118.21