Finding the Third Proportional to 414.50 and 709.50

Step by Step Solution

1. Step 1: Write the proportion equation
   414.50 : 709.50 = 709.50 : x
2. Step 2: Convert to fraction form
   414.50/709.50 = 709.50/x
3. Step 3: Cross multiply
   414.50x = 709.50 × 709.50
4. Step 4: Simplify right side
   414.50x = 503,390.25
5. Step 5: Solve for x
   x = 503,390.25/414.50
6. Step 6: Final answer
   x = 1,214.45