Finding the Third Proportional to 419 and 648.50

Step by Step Solution

1. Step 1: Write the proportion equation
   419 : 648.50 = 648.50 : x
2. Step 2: Convert to fraction form
   419/648.50 = 648.50/x
3. Step 3: Cross multiply
   419x = 648.50 × 648.50
4. Step 4: Simplify right side
   419x = 420,552.25
5. Step 5: Solve for x
   x = 420,552.25/419
6. Step 6: Final answer
   x = 1,003.70