Finding the Third Proportional to 82,206 and 123,322.50

Step by Step Solution

1. Step 1: Write the proportion equation
   82,206 : 123,322.50 = 123,322.50 : x
2. Step 2: Convert to fraction form
   82,206/123,322.50 = 123,322.50/x
3. Step 3: Cross multiply
   82,206x = 123,322.50 × 123,322.50
4. Step 4: Simplify right side
   82,206x = 15,208,439,006.25
5. Step 5: Solve for x
   x = 15,208,439,006.25/82,206
6. Step 6: Final answer
   x = 185,004.00