Finding the Fourth Proportional to 1,024.14, 1,414.86 and 827.31

Step by Step Solution

1. Step 1: Write the proportion equation
   1,024.14 : 1,414.86 = 827.31 : x
2. Step 2: Convert to fraction form
   1,024.14/1,414.86 = 827.31/x
3. Step 3: Cross multiply
   1,024.14x = 1,414.86 × 827.31
4. Step 4: Simplify right side
   1,024.14x = 1,170,527.83
5. Step 5: Solve for x
   x = 1,170,527.83/1,024.14
6. Step 6: Final answer
   x = 1,142.94