Finding the Third Proportional to 111,405 and 256,509

Step by Step Solution

1. Step 1: Write the proportion equation
   111,405 : 256,509 = 256,509 : x
2. Step 2: Convert to fraction form
   111,405/256,509 = 256,509/x
3. Step 3: Cross multiply
   111,405x = 256,509 × 256,509
4. Step 4: Simplify right side
   111,405x = 65,796,867,081
5. Step 5: Solve for x
   x = 65,796,867,081/111,405
6. Step 6: Final answer
   x = 590,609.64