Finding the Third Proportional to 102,377 and 223,666

Step by Step Solution

1. Step 1: Write the proportion equation
   102,377 : 223,666 = 223,666 : x
2. Step 2: Convert to fraction form
   102,377/223,666 = 223,666/x
3. Step 3: Cross multiply
   102,377x = 223,666 × 223,666
4. Step 4: Simplify right side
   102,377x = 50,026,479,556
5. Step 5: Solve for x
   x = 50,026,479,556/102,377
6. Step 6: Final answer
   x = 488,649.59