Finding the Third Proportional to 83,582 and 178,830

Step by Step Solution

1. Step 1: Write the proportion equation
   83,582 : 178,830 = 178,830 : x
2. Step 2: Convert to fraction form
   83,582/178,830 = 178,830/x
3. Step 3: Cross multiply
   83,582x = 178,830 × 178,830
4. Step 4: Simplify right side
   83,582x = 31,980,168,900
5. Step 5: Solve for x
   x = 31,980,168,900/83,582
6. Step 6: Final answer
   x = 382,620.29