Finding the Third Proportional to 37,834 and 82,826

Step by Step Solution

1. Step 1: Write the proportion equation
   37,834 : 82,826 = 82,826 : x
2. Step 2: Convert to fraction form
   37,834/82,826 = 82,826/x
3. Step 3: Cross multiply
   37,834x = 82,826 × 82,826
4. Step 4: Simplify right side
   37,834x = 6,860,146,276
5. Step 5: Solve for x
   x = 6,860,146,276/37,834
6. Step 6: Final answer
   x = 181,322.26