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Finding the Third Proportional to 217,642 and 461,408

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Solution

The third proportional to 217,642 and 461,408 is: 978,199.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    217,642 : 461,408 = 461,408 : x
  2. Step 2: Convert to fraction form
    217,642/461,408 = 461,408/x
  3. Step 3: Cross multiply
    217,642x = 461,408 × 461,408
  4. Step 4: Simplify right side
    217,642x = 212,897,342,464
  5. Step 5: Solve for x
    x = 212,897,342,464/217,642
  6. Step 6: Final answer
    x = 978,199.72

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.