Finding the Third Proportional to 32,814 and 71,642

Step by Step Solution

1. Step 1: Write the proportion equation
   32,814 : 71,642 = 71,642 : x
2. Step 2: Convert to fraction form
   32,814/71,642 = 71,642/x
3. Step 3: Cross multiply
   32,814x = 71,642 × 71,642
4. Step 4: Simplify right side
   32,814x = 5,132,576,164
5. Step 5: Solve for x
   x = 5,132,576,164/32,814
6. Step 6: Final answer
   x = 156,414.22