Finding the Third Proportional to 825.50 and 1,780.50

Step by Step Solution

1. Step 1: Write the proportion equation
   825.50 : 1,780.50 = 1,780.50 : x
2. Step 2: Convert to fraction form
   825.50/1,780.50 = 1,780.50/x
3. Step 3: Cross multiply
   825.50x = 1,780.50 × 1,780.50
4. Step 4: Simplify right side
   825.50x = 3,170,180.25
5. Step 5: Solve for x
   x = 3,170,180.25/825.50
6. Step 6: Final answer
   x = 3,840.32