Finding the Fourth Proportional to 1,853.50, 2,780.61 and 827.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,853.50 : 2,780.61 = 827.50 : x
2. Step 2: Convert to fraction form
   1,853.50/2,780.61 = 827.50/x
3. Step 3: Cross multiply
   1,853.50x = 2,780.61 × 827.50
4. Step 4: Simplify right side
   1,853.50x = 2,300,954.78
5. Step 5: Solve for x
   x = 2,300,954.78/1,853.50
6. Step 6: Final answer
   x = 1,241.41