Finding the Fourth Proportional to 1,005.69, 1,387.88 and 563.61

Step by Step Solution

1. Step 1: Write the proportion equation
   1,005.69 : 1,387.88 = 563.61 : x
2. Step 2: Convert to fraction form
   1,005.69/1,387.88 = 563.61/x
3. Step 3: Cross multiply
   1,005.69x = 1,387.88 × 563.61
4. Step 4: Simplify right side
   1,005.69x = 782,222.91
5. Step 5: Solve for x
   x = 782,222.91/1,005.69
6. Step 6: Final answer
   x = 777.80