Finding the Third Proportional to 37,977 and 83,105

Step by Step Solution

1. Step 1: Write the proportion equation
   37,977 : 83,105 = 83,105 : x
2. Step 2: Convert to fraction form
   37,977/83,105 = 83,105/x
3. Step 3: Cross multiply
   37,977x = 83,105 × 83,105
4. Step 4: Simplify right side
   37,977x = 6,906,441,025
5. Step 5: Solve for x
   x = 6,906,441,025/37,977
6. Step 6: Final answer
   x = 181,858.52