Finding the Third Proportional to 2,082 and 3,165.38

Step by Step Solution

1. Step 1: Write the proportion equation
   2,082 : 3,165.38 = 3,165.38 : x
2. Step 2: Convert to fraction form
   2,082/3,165.38 = 3,165.38/x
3. Step 3: Cross multiply
   2,082x = 3,165.38 × 3,165.38
4. Step 4: Simplify right side
   2,082x = 10,019,598.89
5. Step 5: Solve for x
   x = 10,019,598.89/2,082
6. Step 6: Final answer
   x = 4,812.49