Finding the Third Proportional to 6,780 and 10,406

Step by Step Solution

1. Step 1: Write the proportion equation
   6,780 : 10,406 = 10,406 : x
2. Step 2: Convert to fraction form
   6,780/10,406 = 10,406/x
3. Step 3: Cross multiply
   6,780x = 10,406 × 10,406
4. Step 4: Simplify right side
   6,780x = 108,284,836
5. Step 5: Solve for x
   x = 108,284,836/6,780
6. Step 6: Final answer
   x = 15,971.21