Finding the Fourth Proportional to 1,005.61, 1,387.71 and 563.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,005.61 : 1,387.71 = 563.50 : x
2. Step 2: Convert to fraction form
   1,005.61/1,387.71 = 563.50/x
3. Step 3: Cross multiply
   1,005.61x = 1,387.71 × 563.50
4. Step 4: Simplify right side
   1,005.61x = 781,974.59
5. Step 5: Solve for x
   x = 781,974.59/1,005.61
6. Step 6: Final answer
   x = 777.61