Finding the Fourth Proportional to 1,005.13, 1,387.10 and 563.03

Step by Step Solution

1. Step 1: Write the proportion equation
   1,005.13 : 1,387.10 = 563.03 : x
2. Step 2: Convert to fraction form
   1,005.13/1,387.10 = 563.03/x
3. Step 3: Cross multiply
   1,005.13x = 1,387.10 × 563.03
4. Step 4: Simplify right side
   1,005.13x = 780,978.91
5. Step 5: Solve for x
   x = 780,978.91/1,005.13
6. Step 6: Final answer
   x = 776.99