Finding the Third Proportional to 2,577 and 3,658.50

Step by Step Solution

1. Step 1: Write the proportion equation
   2,577 : 3,658.50 = 3,658.50 : x
2. Step 2: Convert to fraction form
   2,577/3,658.50 = 3,658.50/x
3. Step 3: Cross multiply
   2,577x = 3,658.50 × 3,658.50
4. Step 4: Simplify right side
   2,577x = 13,384,622.25
5. Step 5: Solve for x
   x = 13,384,622.25/2,577
6. Step 6: Final answer
   x = 5,193.88