Finding the Third Proportional to 585.50 and 684.50

Step by Step Solution

1. Step 1: Write the proportion equation
   585.50 : 684.50 = 684.50 : x
2. Step 2: Convert to fraction form
   585.50/684.50 = 684.50/x
3. Step 3: Cross multiply
   585.50x = 684.50 × 684.50
4. Step 4: Simplify right side
   585.50x = 468,540.25
5. Step 5: Solve for x
   x = 468,540.25/585.50
6. Step 6: Final answer
   x = 800.24