Finding the Third Proportional to 419.50 and 568.50

Step by Step Solution

1. Step 1: Write the proportion equation
   419.50 : 568.50 = 568.50 : x
2. Step 2: Convert to fraction form
   419.50/568.50 = 568.50/x
3. Step 3: Cross multiply
   419.50x = 568.50 × 568.50
4. Step 4: Simplify right side
   419.50x = 323,192.25
5. Step 5: Solve for x
   x = 323,192.25/419.50
6. Step 6: Final answer
   x = 770.42