Finding the Third Proportional to 676.50 and 727.50

Step by Step Solution

1. Step 1: Write the proportion equation
   676.50 : 727.50 = 727.50 : x
2. Step 2: Convert to fraction form
   676.50/727.50 = 727.50/x
3. Step 3: Cross multiply
   676.50x = 727.50 × 727.50
4. Step 4: Simplify right side
   676.50x = 529,256.25
5. Step 5: Solve for x
   x = 529,256.25/676.50
6. Step 6: Final answer
   x = 782.34