Finding the Third Proportional to 2,565 and 3,856.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,565 : 3,856.50 = 3,856.50 : x
2. Step 2: Convert to fraction form
   2,565/3,856.50 = 3,856.50/x
3. Step 3: Cross multiply
   2,565x = 3,856.50 × 3,856.50
4. Step 4: Simplify right side
   2,565x = 14,872,592.25
5. Step 5: Solve for x
   x = 14,872,592.25/2,565
6. Step 6: Final answer
   x = 5,798.28