Finding the Fourth Proportional to 1,025.47, 1,538.72 and 409.61

Step by Step Solution

1. Step 1: Write the proportion equation
   1,025.47 : 1,538.72 = 409.61 : x
2. Step 2: Convert to fraction form
   1,025.47/1,538.72 = 409.61/x
3. Step 3: Cross multiply
   1,025.47x = 1,538.72 × 409.61
4. Step 4: Simplify right side
   1,025.47x = 630,275.10
5. Step 5: Solve for x
   x = 630,275.10/1,025.47
6. Step 6: Final answer
   x = 614.62