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Finding the Third Proportional to 100,145 and 217,408

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Solution

The third proportional to 100,145 and 217,408 is: 471,978.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,145 : 217,408 = 217,408 : x
  2. Step 2: Convert to fraction form
    100,145/217,408 = 217,408/x
  3. Step 3: Cross multiply
    100,145x = 217,408 × 217,408
  4. Step 4: Simplify right side
    100,145x = 47,266,238,464
  5. Step 5: Solve for x
    x = 47,266,238,464/100,145
  6. Step 6: Final answer
    x = 471,978.02

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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.