Finding the Third Proportional to 259.50 and 640.50

Step by Step Solution

1. Step 1: Write the proportion equation
   259.50 : 640.50 = 640.50 : x
2. Step 2: Convert to fraction form
   259.50/640.50 = 640.50/x
3. Step 3: Cross multiply
   259.50x = 640.50 × 640.50
4. Step 4: Simplify right side
   259.50x = 410,240.25
5. Step 5: Solve for x
   x = 410,240.25/259.50
6. Step 6: Final answer
   x = 1,580.89