Finding the Third Proportional to 83,780 and 184,470

Step by Step Solution

1. Step 1: Write the proportion equation
   83,780 : 184,470 = 184,470 : x
2. Step 2: Convert to fraction form
   83,780/184,470 = 184,470/x
3. Step 3: Cross multiply
   83,780x = 184,470 × 184,470
4. Step 4: Simplify right side
   83,780x = 34,029,180,900
5. Step 5: Solve for x
   x = 34,029,180,900/83,780
6. Step 6: Final answer
   x = 406,173.08