Finding the Third Proportional to 6,406 and 10,027

Step by Step Solution

1. Step 1: Write the proportion equation
   6,406 : 10,027 = 10,027 : x
2. Step 2: Convert to fraction form
   6,406/10,027 = 10,027/x
3. Step 3: Cross multiply
   6,406x = 10,027 × 10,027
4. Step 4: Simplify right side
   6,406x = 100,540,729
5. Step 5: Solve for x
   x = 100,540,729/6,406
6. Step 6: Final answer
   x = 15,694.78