Finding the Third Proportional to 105,823 and 164,037

Step by Step Solution

1. Step 1: Write the proportion equation
   105,823 : 164,037 = 164,037 : x
2. Step 2: Convert to fraction form
   105,823/164,037 = 164,037/x
3. Step 3: Cross multiply
   105,823x = 164,037 × 164,037
4. Step 4: Simplify right side
   105,823x = 26,908,137,369
5. Step 5: Solve for x
   x = 26,908,137,369/105,823
6. Step 6: Final answer
   x = 254,274.94