Finding the Fourth Proportional to 1,026.56, 1,538.94 and 410.78

Step by Step Solution

1. Step 1: Write the proportion equation
   1,026.56 : 1,538.94 = 410.78 : x
2. Step 2: Convert to fraction form
   1,026.56/1,538.94 = 410.78/x
3. Step 3: Cross multiply
   1,026.56x = 1,538.94 × 410.78
4. Step 4: Simplify right side
   1,026.56x = 632,165.77
5. Step 5: Solve for x
   x = 632,165.77/1,026.56
6. Step 6: Final answer
   x = 615.81