Finding the Third Proportional to 83,580 and 184,656

Step by Step Solution

1. Step 1: Write the proportion equation
   83,580 : 184,656 = 184,656 : x
2. Step 2: Convert to fraction form
   83,580/184,656 = 184,656/x
3. Step 3: Cross multiply
   83,580x = 184,656 × 184,656
4. Step 4: Simplify right side
   83,580x = 34,097,838,336
5. Step 5: Solve for x
   x = 34,097,838,336/83,580
6. Step 6: Final answer
   x = 407,966.48