Finding the Third Proportional to 37,786 and 82,196

Step by Step Solution

1. Step 1: Write the proportion equation
   37,786 : 82,196 = 82,196 : x
2. Step 2: Convert to fraction form
   37,786/82,196 = 82,196/x
3. Step 3: Cross multiply
   37,786x = 82,196 × 82,196
4. Step 4: Simplify right side
   37,786x = 6,756,182,416
5. Step 5: Solve for x
   x = 6,756,182,416/37,786
6. Step 6: Final answer
   x = 178,801.21