Finding the Third Proportional to 419.50 and 648.25

Step by Step Solution

1. Step 1: Write the proportion equation
   419.50 : 648.25 = 648.25 : x
2. Step 2: Convert to fraction form
   419.50/648.25 = 648.25/x
3. Step 3: Cross multiply
   419.50x = 648.25 × 648.25
4. Step 4: Simplify right side
   419.50x = 420,228.06
5. Step 5: Solve for x
   x = 420,228.06/419.50
6. Step 6: Final answer
   x = 1,001.74