Finding the Third Proportional to 2,509.31 and 3,830.63

Step by Step Solution

1. Step 1: Write the proportion equation
   2,509.31 : 3,830.63 = 3,830.63 : x
2. Step 2: Convert to fraction form
   2,509.31/3,830.63 = 3,830.63/x
3. Step 3: Cross multiply
   2,509.31x = 3,830.63 × 3,830.63
4. Step 4: Simplify right side
   2,509.31x = 14,673,687.89
5. Step 5: Solve for x
   x = 14,673,687.89/2,509.31
6. Step 6: Final answer
   x = 5,847.69