Finding the Third Proportional to 411.75 and 586.50

Step by Step Solution

1. Step 1: Write the proportion equation
   411.75 : 586.50 = 586.50 : x
2. Step 2: Convert to fraction form
   411.75/586.50 = 586.50/x
3. Step 3: Cross multiply
   411.75x = 586.50 × 586.50
4. Step 4: Simplify right side
   411.75x = 343,982.25
5. Step 5: Solve for x
   x = 343,982.25/411.75
6. Step 6: Final answer
   x = 835.42