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Finding the Third Proportional to 214,016 and 463,744

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Solution

The third proportional to 214,016 and 463,744 is: 1,004,871.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    214,016 : 463,744 = 463,744 : x
  2. Step 2: Convert to fraction form
    214,016/463,744 = 463,744/x
  3. Step 3: Cross multiply
    214,016x = 463,744 × 463,744
  4. Step 4: Simplify right side
    214,016x = 215,058,497,536
  5. Step 5: Solve for x
    x = 215,058,497,536/214,016
  6. Step 6: Final answer
    x = 1,004,871.12

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.