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Finding the Third Proportional to 419,917 and 432,013

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Solution

The third proportional to 419,917 and 432,013 is: 444,457.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    419,917 : 432,013 = 432,013 : x
  2. Step 2: Convert to fraction form
    419,917/432,013 = 432,013/x
  3. Step 3: Cross multiply
    419,917x = 432,013 × 432,013
  4. Step 4: Simplify right side
    419,917x = 186,635,232,169
  5. Step 5: Solve for x
    x = 186,635,232,169/419,917
  6. Step 6: Final answer
    x = 444,457.43

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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.