Finding the Third Proportional to 772.50 and 826.50

Step by Step Solution

1. Step 1: Write the proportion equation
   772.50 : 826.50 = 826.50 : x
2. Step 2: Convert to fraction form
   772.50/826.50 = 826.50/x
3. Step 3: Cross multiply
   772.50x = 826.50 × 826.50
4. Step 4: Simplify right side
   772.50x = 683,102.25
5. Step 5: Solve for x
   x = 683,102.25/772.50
6. Step 6: Final answer
   x = 884.27