Finding the Third Proportional to 82,378 and 179,864

Step by Step Solution

1. Step 1: Write the proportion equation
   82,378 : 179,864 = 179,864 : x
2. Step 2: Convert to fraction form
   82,378/179,864 = 179,864/x
3. Step 3: Cross multiply
   82,378x = 179,864 × 179,864
4. Step 4: Simplify right side
   82,378x = 32,351,058,496
5. Step 5: Solve for x
   x = 32,351,058,496/82,378
6. Step 6: Final answer
   x = 392,714.78