Finding the Third Proportional to 781.69 and 1,834.69

Step by Step Solution

1. Step 1: Write the proportion equation
   781.69 : 1,834.69 = 1,834.69 : x
2. Step 2: Convert to fraction form
   781.69/1,834.69 = 1,834.69/x
3. Step 3: Cross multiply
   781.69x = 1,834.69 × 1,834.69
4. Step 4: Simplify right side
   781.69x = 3,366,078.22
5. Step 5: Solve for x
   x = 3,366,078.22/781.69
6. Step 6: Final answer
   x = 4,306.17