Finding the Third Proportional to 414 and 654.50

Step by Step Solution

1. Step 1: Write the proportion equation
   414 : 654.50 = 654.50 : x
2. Step 2: Convert to fraction form
   414/654.50 = 654.50/x
3. Step 3: Cross multiply
   414x = 654.50 × 654.50
4. Step 4: Simplify right side
   414x = 428,370.25
5. Step 5: Solve for x
   x = 428,370.25/414
6. Step 6: Final answer
   x = 1,034.71