Finding the Third Proportional to 85,824 and 189,098

Step by Step Solution

1. Step 1: Write the proportion equation
   85,824 : 189,098 = 189,098 : x
2. Step 2: Convert to fraction form
   85,824/189,098 = 189,098/x
3. Step 3: Cross multiply
   85,824x = 189,098 × 189,098
4. Step 4: Simplify right side
   85,824x = 35,758,053,604
5. Step 5: Solve for x
   x = 35,758,053,604/85,824
6. Step 6: Final answer
   x = 416,643.99