Finding the Fourth Proportional to 766.50, 1,148.72 and 419.31

Step by Step Solution

1. Step 1: Write the proportion equation
   766.50 : 1,148.72 = 419.31 : x
2. Step 2: Convert to fraction form
   766.50/1,148.72 = 419.31/x
3. Step 3: Cross multiply
   766.50x = 1,148.72 × 419.31
4. Step 4: Simplify right side
   766.50x = 481,667.69
5. Step 5: Solve for x
   x = 481,667.69/766.50
6. Step 6: Final answer
   x = 628.40