Finding the Third Proportional to 509.50 and 620.50

Step by Step Solution

1. Step 1: Write the proportion equation
   509.50 : 620.50 = 620.50 : x
2. Step 2: Convert to fraction form
   509.50/620.50 = 620.50/x
3. Step 3: Cross multiply
   509.50x = 620.50 × 620.50
4. Step 4: Simplify right side
   509.50x = 385,020.25
5. Step 5: Solve for x
   x = 385,020.25/509.50
6. Step 6: Final answer
   x = 755.68