Finding the Fourth Proportional to 1,109.34, 1,663.83 and 459.90

Step by Step Solution

1. Step 1: Write the proportion equation
   1,109.34 : 1,663.83 = 459.90 : x
2. Step 2: Convert to fraction form
   1,109.34/1,663.83 = 459.90/x
3. Step 3: Cross multiply
   1,109.34x = 1,663.83 × 459.90
4. Step 4: Simplify right side
   1,109.34x = 765,195.42
5. Step 5: Solve for x
   x = 765,195.42/1,109.34
6. Step 6: Final answer
   x = 689.78