Finding the Third Proportional to 5,097.50 and 7,697.50

Step by Step Solution

1. Step 1: Write the proportion equation
   5,097.50 : 7,697.50 = 7,697.50 : x
2. Step 2: Convert to fraction form
   5,097.50/7,697.50 = 7,697.50/x
3. Step 3: Cross multiply
   5,097.50x = 7,697.50 × 7,697.50
4. Step 4: Simplify right side
   5,097.50x = 59,251,506.25
5. Step 5: Solve for x
   x = 59,251,506.25/5,097.50
6. Step 6: Final answer
   x = 11,623.64