Finding the Third Proportional to 5,188 and 7,764.50

Step by Step Solution

1. Step 1: Write the proportion equation
   5,188 : 7,764.50 = 7,764.50 : x
2. Step 2: Convert to fraction form
   5,188/7,764.50 = 7,764.50/x
3. Step 3: Cross multiply
   5,188x = 7,764.50 × 7,764.50
4. Step 4: Simplify right side
   5,188x = 60,287,460.25
5. Step 5: Solve for x
   x = 60,287,460.25/5,188
6. Step 6: Final answer
   x = 11,620.56