Finding the Third Proportional to 2,082 and 2,785.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,082 : 2,785.50 = 2,785.50 : x
2. Step 2: Convert to fraction form
   2,082/2,785.50 = 2,785.50/x
3. Step 3: Cross multiply
   2,082x = 2,785.50 × 2,785.50
4. Step 4: Simplify right side
   2,082x = 7,759,010.25
5. Step 5: Solve for x
   x = 7,759,010.25/2,082
6. Step 6: Final answer
   x = 3,726.71