Finding the Third Proportional to 506.50 and 643.50

Step by Step Solution

1. Step 1: Write the proportion equation
   506.50 : 643.50 = 643.50 : x
2. Step 2: Convert to fraction form
   506.50/643.50 = 643.50/x
3. Step 3: Cross multiply
   506.50x = 643.50 × 643.50
4. Step 4: Simplify right side
   506.50x = 414,092.25
5. Step 5: Solve for x
   x = 414,092.25/506.50
6. Step 6: Final answer
   x = 817.56