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Finding the Third Proportional to 100,147 and 217,412

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Solution

The third proportional to 100,147 and 217,412 is: 471,985.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,147 : 217,412 = 217,412 : x
  2. Step 2: Convert to fraction form
    100,147/217,412 = 217,412/x
  3. Step 3: Cross multiply
    100,147x = 217,412 × 217,412
  4. Step 4: Simplify right side
    100,147x = 47,267,977,744
  5. Step 5: Solve for x
    x = 47,267,977,744/100,147
  6. Step 6: Final answer
    x = 471,985.96

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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.