Finding the Third Proportional to 82,185 and 177,222

Step by Step Solution

1. Step 1: Write the proportion equation
   82,185 : 177,222 = 177,222 : x
2. Step 2: Convert to fraction form
   82,185/177,222 = 177,222/x
3. Step 3: Cross multiply
   82,185x = 177,222 × 177,222
4. Step 4: Simplify right side
   82,185x = 31,407,637,284
5. Step 5: Solve for x
   x = 31,407,637,284/82,185
6. Step 6: Final answer
   x = 382,157.78