Finding the Third Proportional to 5,192 and 7,766.50

Step by Step Solution

1. Step 1: Write the proportion equation
   5,192 : 7,766.50 = 7,766.50 : x
2. Step 2: Convert to fraction form
   5,192/7,766.50 = 7,766.50/x
3. Step 3: Cross multiply
   5,192x = 7,766.50 × 7,766.50
4. Step 4: Simplify right side
   5,192x = 60,318,522.25
5. Step 5: Solve for x
   x = 60,318,522.25/5,192
6. Step 6: Final answer
   x = 11,617.59