Finding the Third Proportional to 78,384 and 172,320

Step by Step Solution

1. Step 1: Write the proportion equation
   78,384 : 172,320 = 172,320 : x
2. Step 2: Convert to fraction form
   78,384/172,320 = 172,320/x
3. Step 3: Cross multiply
   78,384x = 172,320 × 172,320
4. Step 4: Simplify right side
   78,384x = 29,694,182,400
5. Step 5: Solve for x
   x = 29,694,182,400/78,384
6. Step 6: Final answer
   x = 378,829.64