Finding the Third Proportional to 209.50 and 384.50

Step by Step Solution

1. Step 1: Write the proportion equation
   209.50 : 384.50 = 384.50 : x
2. Step 2: Convert to fraction form
   209.50/384.50 = 384.50/x
3. Step 3: Cross multiply
   209.50x = 384.50 × 384.50
4. Step 4: Simplify right side
   209.50x = 147,840.25
5. Step 5: Solve for x
   x = 147,840.25/209.50
6. Step 6: Final answer
   x = 705.68