Finding the Third Proportional to 409.50 and 580.50

Step by Step Solution

1. Step 1: Write the proportion equation
   409.50 : 580.50 = 580.50 : x
2. Step 2: Convert to fraction form
   409.50/580.50 = 580.50/x
3. Step 3: Cross multiply
   409.50x = 580.50 × 580.50
4. Step 4: Simplify right side
   409.50x = 336,980.25
5. Step 5: Solve for x
   x = 336,980.25/409.50
6. Step 6: Final answer
   x = 822.91