Finding the Third Proportional to 410 and 584.50

Step by Step Solution

1. Step 1: Write the proportion equation
   410 : 584.50 = 584.50 : x
2. Step 2: Convert to fraction form
   410/584.50 = 584.50/x
3. Step 3: Cross multiply
   410x = 584.50 × 584.50
4. Step 4: Simplify right side
   410x = 341,640.25
5. Step 5: Solve for x
   x = 341,640.25/410
6. Step 6: Final answer
   x = 833.27