Finding the Third Proportional to 177.50 and 381.59

Step by Step Solution

1. Step 1: Write the proportion equation
   177.50 : 381.59 = 381.59 : x
2. Step 2: Convert to fraction form
   177.50/381.59 = 381.59/x
3. Step 3: Cross multiply
   177.50x = 381.59 × 381.59
4. Step 4: Simplify right side
   177.50x = 145,607.83
5. Step 5: Solve for x
   x = 145,607.83/177.50
6. Step 6: Final answer
   x = 820.31