Finding the Third Proportional to 37,966 and 83,082

Step by Step Solution

1. Step 1: Write the proportion equation
   37,966 : 83,082 = 83,082 : x
2. Step 2: Convert to fraction form
   37,966/83,082 = 83,082/x
3. Step 3: Cross multiply
   37,966x = 83,082 × 83,082
4. Step 4: Simplify right side
   37,966x = 6,902,618,724
5. Step 5: Solve for x
   x = 6,902,618,724/37,966
6. Step 6: Final answer
   x = 181,810.53