Finding the Third Proportional to 102,048 and 223,824

Step by Step Solution

1. Step 1: Write the proportion equation
   102,048 : 223,824 = 223,824 : x
2. Step 2: Convert to fraction form
   102,048/223,824 = 223,824/x
3. Step 3: Cross multiply
   102,048x = 223,824 × 223,824
4. Step 4: Simplify right side
   102,048x = 50,097,182,976
5. Step 5: Solve for x
   x = 50,097,182,976/102,048
6. Step 6: Final answer
   x = 490,917.83