Finding the Third Proportional to 772.50 and 796.50

Step by Step Solution

1. Step 1: Write the proportion equation
   772.50 : 796.50 = 796.50 : x
2. Step 2: Convert to fraction form
   772.50/796.50 = 796.50/x
3. Step 3: Cross multiply
   772.50x = 796.50 × 796.50
4. Step 4: Simplify right side
   772.50x = 634,412.25
5. Step 5: Solve for x
   x = 634,412.25/772.50
6. Step 6: Final answer
   x = 821.25