Finding the Third Proportional to 423.50 and 509.50

Step by Step Solution

1. Step 1: Write the proportion equation
   423.50 : 509.50 = 509.50 : x
2. Step 2: Convert to fraction form
   423.50/509.50 = 509.50/x
3. Step 3: Cross multiply
   423.50x = 509.50 × 509.50
4. Step 4: Simplify right side
   423.50x = 259,590.25
5. Step 5: Solve for x
   x = 259,590.25/423.50
6. Step 6: Final answer
   x = 612.96