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Finding the Third Proportional to 212,486 and 463,609

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Solution

The third proportional to 212,486 and 463,609 is: 1,011,517.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,486 : 463,609 = 463,609 : x
  2. Step 2: Convert to fraction form
    212,486/463,609 = 463,609/x
  3. Step 3: Cross multiply
    212,486x = 463,609 × 463,609
  4. Step 4: Simplify right side
    212,486x = 214,933,304,881
  5. Step 5: Solve for x
    x = 214,933,304,881/212,486
  6. Step 6: Final answer
    x = 1,011,517.49

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.