Finding the Third Proportional to 682.50 and 727.50

Step by Step Solution

1. Step 1: Write the proportion equation
   682.50 : 727.50 = 727.50 : x
2. Step 2: Convert to fraction form
   682.50/727.50 = 727.50/x
3. Step 3: Cross multiply
   682.50x = 727.50 × 727.50
4. Step 4: Simplify right side
   682.50x = 529,256.25
5. Step 5: Solve for x
   x = 529,256.25/682.50
6. Step 6: Final answer
   x = 775.47