Finding the Third Proportional to 82,830 and 180,384

Step by Step Solution

1. Step 1: Write the proportion equation
   82,830 : 180,384 = 180,384 : x
2. Step 2: Convert to fraction form
   82,830/180,384 = 180,384/x
3. Step 3: Cross multiply
   82,830x = 180,384 × 180,384
4. Step 4: Simplify right side
   82,830x = 32,538,387,456
5. Step 5: Solve for x
   x = 32,538,387,456/82,830
6. Step 6: Final answer
   x = 392,833.36