Finding the Third Proportional to 105,822 and 164,196

Step by Step Solution

1. Step 1: Write the proportion equation
   105,822 : 164,196 = 164,196 : x
2. Step 2: Convert to fraction form
   105,822/164,196 = 164,196/x
3. Step 3: Cross multiply
   105,822x = 164,196 × 164,196
4. Step 4: Simplify right side
   105,822x = 26,960,326,416
5. Step 5: Solve for x
   x = 26,960,326,416/105,822
6. Step 6: Final answer
   x = 254,770.52