Finding the Third Proportional to 417.56 and 463.69

Step by Step Solution

1. Step 1: Write the proportion equation
   417.56 : 463.69 = 463.69 : x
2. Step 2: Convert to fraction form
   417.56/463.69 = 463.69/x
3. Step 3: Cross multiply
   417.56x = 463.69 × 463.69
4. Step 4: Simplify right side
   417.56x = 215,006.10
5. Step 5: Solve for x
   x = 215,006.10/417.56
6. Step 6: Final answer
   x = 514.91