Finding the Third Proportional to 5,188.50 and 7,786.25

Step by Step Solution

1. Step 1: Write the proportion equation
   5,188.50 : 7,786.25 = 7,786.25 : x
2. Step 2: Convert to fraction form
   5,188.50/7,786.25 = 7,786.25/x
3. Step 3: Cross multiply
   5,188.50x = 7,786.25 × 7,786.25
4. Step 4: Simplify right side
   5,188.50x = 60,625,689.06
5. Step 5: Solve for x
   x = 60,625,689.06/5,188.50
6. Step 6: Final answer
   x = 11,684.63