Finding the Third Proportional to 82,419 and 177,978

Step by Step Solution

1. Step 1: Write the proportion equation
   82,419 : 177,978 = 177,978 : x
2. Step 2: Convert to fraction form
   82,419/177,978 = 177,978/x
3. Step 3: Cross multiply
   82,419x = 177,978 × 177,978
4. Step 4: Simplify right side
   82,419x = 31,676,168,484
5. Step 5: Solve for x
   x = 31,676,168,484/82,419
6. Step 6: Final answer
   x = 384,330.90