Finding the Third Proportional to 2,138 and 4,664.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,138 : 4,664.50 = 4,664.50 : x
2. Step 2: Convert to fraction form
   2,138/4,664.50 = 4,664.50/x
3. Step 3: Cross multiply
   2,138x = 4,664.50 × 4,664.50
4. Step 4: Simplify right side
   2,138x = 21,757,560.25
5. Step 5: Solve for x
   x = 21,757,560.25/2,138
6. Step 6: Final answer
   x = 10,176.60