Finding the Third Proportional to 2,537.89 and 3,785.80

Step by Step Solution

1. Step 1: Write the proportion equation
   2,537.89 : 3,785.80 = 3,785.80 : x
2. Step 2: Convert to fraction form
   2,537.89/3,785.80 = 3,785.80/x
3. Step 3: Cross multiply
   2,537.89x = 3,785.80 × 3,785.80
4. Step 4: Simplify right side
   2,537.89x = 14,332,287.56
5. Step 5: Solve for x
   x = 14,332,287.56/2,537.89
6. Step 6: Final answer
   x = 5,647.31