Finding the Third Proportional to 83,624 and 178,586

Step by Step Solution

1. Step 1: Write the proportion equation
   83,624 : 178,586 = 178,586 : x
2. Step 2: Convert to fraction form
   83,624/178,586 = 178,586/x
3. Step 3: Cross multiply
   83,624x = 178,586 × 178,586
4. Step 4: Simplify right side
   83,624x = 31,892,959,396
5. Step 5: Solve for x
   x = 31,892,959,396/83,624
6. Step 6: Final answer
   x = 381,385.24