Finding the Third Proportional to 35,676 and 77,184

Step by Step Solution

1. Step 1: Write the proportion equation
   35,676 : 77,184 = 77,184 : x
2. Step 2: Convert to fraction form
   35,676/77,184 = 77,184/x
3. Step 3: Cross multiply
   35,676x = 77,184 × 77,184
4. Step 4: Simplify right side
   35,676x = 5,957,369,856
5. Step 5: Solve for x
   x = 5,957,369,856/35,676
6. Step 6: Final answer
   x = 166,985.36