Finding the Third Proportional to 83,168 and 177,784

Step by Step Solution

1. Step 1: Write the proportion equation
   83,168 : 177,784 = 177,784 : x
2. Step 2: Convert to fraction form
   83,168/177,784 = 177,784/x
3. Step 3: Cross multiply
   83,168x = 177,784 × 177,784
4. Step 4: Simplify right side
   83,168x = 31,607,150,656
5. Step 5: Solve for x
   x = 31,607,150,656/83,168
6. Step 6: Final answer
   x = 380,039.81