Finding the Third Proportional to 583.50 and 820.50

Step by Step Solution

1. Step 1: Write the proportion equation
   583.50 : 820.50 = 820.50 : x
2. Step 2: Convert to fraction form
   583.50/820.50 = 820.50/x
3. Step 3: Cross multiply
   583.50x = 820.50 × 820.50
4. Step 4: Simplify right side
   583.50x = 673,220.25
5. Step 5: Solve for x
   x = 673,220.25/583.50
6. Step 6: Final answer
   x = 1,153.76