Finding the Third Proportional to 123,414 and 256,527

Step by Step Solution

1. Step 1: Write the proportion equation
   123,414 : 256,527 = 256,527 : x
2. Step 2: Convert to fraction form
   123,414/256,527 = 256,527/x
3. Step 3: Cross multiply
   123,414x = 256,527 × 256,527
4. Step 4: Simplify right side
   123,414x = 65,806,101,729
5. Step 5: Solve for x
   x = 65,806,101,729/123,414
6. Step 6: Final answer
   x = 533,214.24