Finding the Third Proportional to 772.50 and 1,648

Step by Step Solution

1. Step 1: Write the proportion equation
   772.50 : 1,648 = 1,648 : x
2. Step 2: Convert to fraction form
   772.50/1,648 = 1,648/x
3. Step 3: Cross multiply
   772.50x = 1,648 × 1,648
4. Step 4: Simplify right side
   772.50x = 2,715,904
5. Step 5: Solve for x
   x = 2,715,904/772.50
6. Step 6: Final answer
   x = 3,515.73