Finding the Third Proportional to 83,066 and 177,007

Step by Step Solution

1. Step 1: Write the proportion equation
   83,066 : 177,007 = 177,007 : x
2. Step 2: Convert to fraction form
   83,066/177,007 = 177,007/x
3. Step 3: Cross multiply
   83,066x = 177,007 × 177,007
4. Step 4: Simplify right side
   83,066x = 31,331,478,049
5. Step 5: Solve for x
   x = 31,331,478,049/83,066
6. Step 6: Final answer
   x = 377,187.75