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Finding the Third Proportional to 256,415 and 398,064

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Solution

The third proportional to 256,415 and 398,064 is: 617,962.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,415 : 398,064 = 398,064 : x
  2. Step 2: Convert to fraction form
    256,415/398,064 = 398,064/x
  3. Step 3: Cross multiply
    256,415x = 398,064 × 398,064
  4. Step 4: Simplify right side
    256,415x = 158,454,948,096
  5. Step 5: Solve for x
    x = 158,454,948,096/256,415
  6. Step 6: Final answer
    x = 617,962.87

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.