Finding the Third Proportional to 706.78 and 769.78

Step by Step Solution

1. Step 1: Write the proportion equation
   706.78 : 769.78 = 769.78 : x
2. Step 2: Convert to fraction form
   706.78/769.78 = 769.78/x
3. Step 3: Cross multiply
   706.78x = 769.78 × 769.78
4. Step 4: Simplify right side
   706.78x = 592,563.17
5. Step 5: Solve for x
   x = 592,563.17/706.78
6. Step 6: Final answer
   x = 838.40