Finding the Third Proportional to 37,801 and 82,783

Step by Step Solution

1. Step 1: Write the proportion equation
   37,801 : 82,783 = 82,783 : x
2. Step 2: Convert to fraction form
   37,801/82,783 = 82,783/x
3. Step 3: Cross multiply
   37,801x = 82,783 × 82,783
4. Step 4: Simplify right side
   37,801x = 6,853,025,089
5. Step 5: Solve for x
   x = 6,853,025,089/37,801
6. Step 6: Final answer
   x = 181,292.16