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Finding the Third Proportional to 419,919 and 432,015

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Solution

The third proportional to 419,919 and 432,015 is: 444,459.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    419,919 : 432,015 = 432,015 : x
  2. Step 2: Convert to fraction form
    419,919/432,015 = 432,015/x
  3. Step 3: Cross multiply
    419,919x = 432,015 × 432,015
  4. Step 4: Simplify right side
    419,919x = 186,636,960,225
  5. Step 5: Solve for x
    x = 186,636,960,225/419,919
  6. Step 6: Final answer
    x = 444,459.43

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Why These Related Problems?

These problems maintain the same ratio (1.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.