Finding the Third Proportional to 82,642 and 178,532

Step by Step Solution

1. Step 1: Write the proportion equation
   82,642 : 178,532 = 178,532 : x
2. Step 2: Convert to fraction form
   82,642/178,532 = 178,532/x
3. Step 3: Cross multiply
   82,642x = 178,532 × 178,532
4. Step 4: Simplify right side
   82,642x = 31,873,675,024
5. Step 5: Solve for x
   x = 31,873,675,024/82,642
6. Step 6: Final answer
   x = 385,683.73