Finding the Third Proportional to 37,824 and 82,194

Step by Step Solution

1. Step 1: Write the proportion equation
   37,824 : 82,194 = 82,194 : x
2. Step 2: Convert to fraction form
   37,824/82,194 = 82,194/x
3. Step 3: Cross multiply
   37,824x = 82,194 × 82,194
4. Step 4: Simplify right side
   37,824x = 6,755,853,636
5. Step 5: Solve for x
   x = 6,755,853,636/37,824
6. Step 6: Final answer
   x = 178,612.88