Finding the Third Proportional to 383.50 and 678.50

Step by Step Solution

1. Step 1: Write the proportion equation
   383.50 : 678.50 = 678.50 : x
2. Step 2: Convert to fraction form
   383.50/678.50 = 678.50/x
3. Step 3: Cross multiply
   383.50x = 678.50 × 678.50
4. Step 4: Simplify right side
   383.50x = 460,362.25
5. Step 5: Solve for x
   x = 460,362.25/383.50
6. Step 6: Final answer
   x = 1,200.42