Finding the Third Proportional to 85,777 and 189,005

Step by Step Solution

1. Step 1: Write the proportion equation
   85,777 : 189,005 = 189,005 : x
2. Step 2: Convert to fraction form
   85,777/189,005 = 189,005/x
3. Step 3: Cross multiply
   85,777x = 189,005 × 189,005
4. Step 4: Simplify right side
   85,777x = 35,722,890,025
5. Step 5: Solve for x
   x = 35,722,890,025/85,777
6. Step 6: Final answer
   x = 416,462.34