Finding the Third Proportional to 2,138 and 4,678

Step by Step Solution

1. Step 1: Write the proportion equation
   2,138 : 4,678 = 4,678 : x
2. Step 2: Convert to fraction form
   2,138/4,678 = 4,678/x
3. Step 3: Cross multiply
   2,138x = 4,678 × 4,678
4. Step 4: Simplify right side
   2,138x = 21,883,684
5. Step 5: Solve for x
   x = 21,883,684/2,138
6. Step 6: Final answer
   x = 10,235.59