Finding the Third Proportional to 463.50 and 769.50

Step by Step Solution

1. Step 1: Write the proportion equation
   463.50 : 769.50 = 769.50 : x
2. Step 2: Convert to fraction form
   463.50/769.50 = 769.50/x
3. Step 3: Cross multiply
   463.50x = 769.50 × 769.50
4. Step 4: Simplify right side
   463.50x = 592,130.25
5. Step 5: Solve for x
   x = 592,130.25/463.50
6. Step 6: Final answer
   x = 1,277.52