Finding the Third Proportional to 7,834.50 and 8,698.50

Step by Step Solution

1. Step 1: Write the proportion equation
   7,834.50 : 8,698.50 = 8,698.50 : x
2. Step 2: Convert to fraction form
   7,834.50/8,698.50 = 8,698.50/x
3. Step 3: Cross multiply
   7,834.50x = 8,698.50 × 8,698.50
4. Step 4: Simplify right side
   7,834.50x = 75,663,902.25
5. Step 5: Solve for x
   x = 75,663,902.25/7,834.50
6. Step 6: Final answer
   x = 9,657.78