Finding the Third Proportional to 35,834 and 83,677

Step by Step Solution

1. Step 1: Write the proportion equation
   35,834 : 83,677 = 83,677 : x
2. Step 2: Convert to fraction form
   35,834/83,677 = 83,677/x
3. Step 3: Cross multiply
   35,834x = 83,677 × 83,677
4. Step 4: Simplify right side
   35,834x = 7,001,840,329
5. Step 5: Solve for x
   x = 7,001,840,329/35,834
6. Step 6: Final answer
   x = 195,396.56