Finding the Third Proportional to 100,642 and 205,654

Step by Step Solution

1. Step 1: Write the proportion equation
   100,642 : 205,654 = 205,654 : x
2. Step 2: Convert to fraction form
   100,642/205,654 = 205,654/x
3. Step 3: Cross multiply
   100,642x = 205,654 × 205,654
4. Step 4: Simplify right side
   100,642x = 42,293,567,716
5. Step 5: Solve for x
   x = 42,293,567,716/100,642
6. Step 6: Final answer
   x = 420,237.75