Finding the Third Proportional to 462.38 and 678.38

Step by Step Solution

1. Step 1: Write the proportion equation
   462.38 : 678.38 = 678.38 : x
2. Step 2: Convert to fraction form
   462.38/678.38 = 678.38/x
3. Step 3: Cross multiply
   462.38x = 678.38 × 678.38
4. Step 4: Simplify right side
   462.38x = 460,192.64
5. Step 5: Solve for x
   x = 460,192.64/462.38
6. Step 6: Final answer
   x = 995.28