Finding the Third Proportional to 82.13 and 193.50

Step by Step Solution

1. Step 1: Write the proportion equation
   82.13 : 193.50 = 193.50 : x
2. Step 2: Convert to fraction form
   82.13/193.50 = 193.50/x
3. Step 3: Cross multiply
   82.13x = 193.50 × 193.50
4. Step 4: Simplify right side
   82.13x = 37,442.25
5. Step 5: Solve for x
   x = 37,442.25/82.13
6. Step 6: Final answer
   x = 455.92