Finding the Third Proportional to 509.50 and 601.50

Step by Step Solution

1. Step 1: Write the proportion equation
   509.50 : 601.50 = 601.50 : x
2. Step 2: Convert to fraction form
   509.50/601.50 = 601.50/x
3. Step 3: Cross multiply
   509.50x = 601.50 × 601.50
4. Step 4: Simplify right side
   509.50x = 361,802.25
5. Step 5: Solve for x
   x = 361,802.25/509.50
6. Step 6: Final answer
   x = 710.11