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Finding the Third Proportional to 256,871 and 409,098

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Solution

The third proportional to 256,871 and 409,098 is: 651,537.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,871 : 409,098 = 409,098 : x
  2. Step 2: Convert to fraction form
    256,871/409,098 = 409,098/x
  3. Step 3: Cross multiply
    256,871x = 409,098 × 409,098
  4. Step 4: Simplify right side
    256,871x = 167,361,173,604
  5. Step 5: Solve for x
    x = 167,361,173,604/256,871
  6. Step 6: Final answer
    x = 651,537.83

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.