Finding the Third Proportional to 419.25 and 559.50

Step by Step Solution

1. Step 1: Write the proportion equation
   419.25 : 559.50 = 559.50 : x
2. Step 2: Convert to fraction form
   419.25/559.50 = 559.50/x
3. Step 3: Cross multiply
   419.25x = 559.50 × 559.50
4. Step 4: Simplify right side
   419.25x = 313,040.25
5. Step 5: Solve for x
   x = 313,040.25/419.25
6. Step 6: Final answer
   x = 746.67