Finding the Third Proportional to 82,377 and 179,856

Step by Step Solution

1. Step 1: Write the proportion equation
   82,377 : 179,856 = 179,856 : x
2. Step 2: Convert to fraction form
   82,377/179,856 = 179,856/x
3. Step 3: Cross multiply
   82,377x = 179,856 × 179,856
4. Step 4: Simplify right side
   82,377x = 32,348,180,736
5. Step 5: Solve for x
   x = 32,348,180,736/82,377
6. Step 6: Final answer
   x = 392,684.62