Finding the Third Proportional to 584.50 and 629.50

Step by Step Solution

1. Step 1: Write the proportion equation
   584.50 : 629.50 = 629.50 : x
2. Step 2: Convert to fraction form
   584.50/629.50 = 629.50/x
3. Step 3: Cross multiply
   584.50x = 629.50 × 629.50
4. Step 4: Simplify right side
   584.50x = 396,270.25
5. Step 5: Solve for x
   x = 396,270.25/584.50
6. Step 6: Final answer
   x = 677.96