Finding the Third Proportional to 37,802 and 82,164

Step by Step Solution

1. Step 1: Write the proportion equation
   37,802 : 82,164 = 82,164 : x
2. Step 2: Convert to fraction form
   37,802/82,164 = 82,164/x
3. Step 3: Cross multiply
   37,802x = 82,164 × 82,164
4. Step 4: Simplify right side
   37,802x = 6,750,922,896
5. Step 5: Solve for x
   x = 6,750,922,896/37,802
6. Step 6: Final answer
   x = 178,586.39