Finding the Third Proportional to 82,823 and 178,759

Step by Step Solution

1. Step 1: Write the proportion equation
   82,823 : 178,759 = 178,759 : x
2. Step 2: Convert to fraction form
   82,823/178,759 = 178,759/x
3. Step 3: Cross multiply
   82,823x = 178,759 × 178,759
4. Step 4: Simplify right side
   82,823x = 31,954,780,081
5. Step 5: Solve for x
   x = 31,954,780,081/82,823
6. Step 6: Final answer
   x = 385,820.12