Finding the Third Proportional to 419.50 and 685.50

Step by Step Solution

1. Step 1: Write the proportion equation
   419.50 : 685.50 = 685.50 : x
2. Step 2: Convert to fraction form
   419.50/685.50 = 685.50/x
3. Step 3: Cross multiply
   419.50x = 685.50 × 685.50
4. Step 4: Simplify right side
   419.50x = 469,910.25
5. Step 5: Solve for x
   x = 469,910.25/419.50
6. Step 6: Final answer
   x = 1,120.17