Finding the Third Proportional to 85,876 and 186,538

Step by Step Solution

1. Step 1: Write the proportion equation
   85,876 : 186,538 = 186,538 : x
2. Step 2: Convert to fraction form
   85,876/186,538 = 186,538/x
3. Step 3: Cross multiply
   85,876x = 186,538 × 186,538
4. Step 4: Simplify right side
   85,876x = 34,796,425,444
5. Step 5: Solve for x
   x = 34,796,425,444/85,876
6. Step 6: Final answer
   x = 405,193.83