Finding the Third Proportional to 463.50 and 511.88

Step by Step Solution

1. Step 1: Write the proportion equation
   463.50 : 511.88 = 511.88 : x
2. Step 2: Convert to fraction form
   463.50/511.88 = 511.88/x
3. Step 3: Cross multiply
   463.50x = 511.88 × 511.88
4. Step 4: Simplify right side
   463.50x = 262,016.02
5. Step 5: Solve for x
   x = 262,016.02/463.50
6. Step 6: Final answer
   x = 565.30