Finding the Third Proportional to 2,577 and 5,336.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,577 : 5,336.50 = 5,336.50 : x
2. Step 2: Convert to fraction form
   2,577/5,336.50 = 5,336.50/x
3. Step 3: Cross multiply
   2,577x = 5,336.50 × 5,336.50
4. Step 4: Simplify right side
   2,577x = 28,478,232.25
5. Step 5: Solve for x
   x = 28,478,232.25/2,577
6. Step 6: Final answer
   x = 11,050.92