Finding the Third Proportional to 217.50 and 409.50

Step by Step Solution

1. Step 1: Write the proportion equation
   217.50 : 409.50 = 409.50 : x
2. Step 2: Convert to fraction form
   217.50/409.50 = 409.50/x
3. Step 3: Cross multiply
   217.50x = 409.50 × 409.50
4. Step 4: Simplify right side
   217.50x = 167,690.25
5. Step 5: Solve for x
   x = 167,690.25/217.50
6. Step 6: Final answer
   x = 770.99