Finding the Third Proportional to 5,826 and 7,834.50

Step by Step Solution

1. Step 1: Write the proportion equation
   5,826 : 7,834.50 = 7,834.50 : x
2. Step 2: Convert to fraction form
   5,826/7,834.50 = 7,834.50/x
3. Step 3: Cross multiply
   5,826x = 7,834.50 × 7,834.50
4. Step 4: Simplify right side
   5,826x = 61,379,390.25
5. Step 5: Solve for x
   x = 61,379,390.25/5,826
6. Step 6: Final answer
   x = 10,535.43