Finding the Third Proportional to 419.50 and 638.50

Step by Step Solution

1. Step 1: Write the proportion equation
   419.50 : 638.50 = 638.50 : x
2. Step 2: Convert to fraction form
   419.50/638.50 = 638.50/x
3. Step 3: Cross multiply
   419.50x = 638.50 × 638.50
4. Step 4: Simplify right side
   419.50x = 407,682.25
5. Step 5: Solve for x
   x = 407,682.25/419.50
6. Step 6: Final answer
   x = 971.83