Finding the Third Proportional to 82,091 and 177,007

Step by Step Solution

1. Step 1: Write the proportion equation
   82,091 : 177,007 = 177,007 : x
2. Step 2: Convert to fraction form
   82,091/177,007 = 177,007/x
3. Step 3: Cross multiply
   82,091x = 177,007 × 177,007
4. Step 4: Simplify right side
   82,091x = 31,331,478,049
5. Step 5: Solve for x
   x = 31,331,478,049/82,091
6. Step 6: Final answer
   x = 381,667.64