Finding the Third Proportional to 1,401 and 1,540.50

Step by Step Solution

1. Step 1: Write the proportion equation
   1,401 : 1,540.50 = 1,540.50 : x
2. Step 2: Convert to fraction form
   1,401/1,540.50 = 1,540.50/x
3. Step 3: Cross multiply
   1,401x = 1,540.50 × 1,540.50
4. Step 4: Simplify right side
   1,401x = 2,373,140.25
5. Step 5: Solve for x
   x = 2,373,140.25/1,401
6. Step 6: Final answer
   x = 1,693.89