Finding the Third Proportional to 37,805 and 82,414

Step by Step Solution

1. Step 1: Write the proportion equation
   37,805 : 82,414 = 82,414 : x
2. Step 2: Convert to fraction form
   37,805/82,414 = 82,414/x
3. Step 3: Cross multiply
   37,805x = 82,414 × 82,414
4. Step 4: Simplify right side
   37,805x = 6,792,067,396
5. Step 5: Solve for x
   x = 6,792,067,396/37,805
6. Step 6: Final answer
   x = 179,660.56