Finding the Third Proportional to 825.38 and 978.38

Step by Step Solution

1. Step 1: Write the proportion equation
   825.38 : 978.38 = 978.38 : x
2. Step 2: Convert to fraction form
   825.38/978.38 = 978.38/x
3. Step 3: Cross multiply
   825.38x = 978.38 × 978.38
4. Step 4: Simplify right side
   825.38x = 957,217.64
5. Step 5: Solve for x
   x = 957,217.64/825.38
6. Step 6: Final answer
   x = 1,159.74