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Finding the Third Proportional to 289,469 and 413,563

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Solution

The third proportional to 289,469 and 413,563 is: 590,855.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    289,469 : 413,563 = 413,563 : x
  2. Step 2: Convert to fraction form
    289,469/413,563 = 413,563/x
  3. Step 3: Cross multiply
    289,469x = 413,563 × 413,563
  4. Step 4: Simplify right side
    289,469x = 171,034,354,969
  5. Step 5: Solve for x
    x = 171,034,354,969/289,469
  6. Step 6: Final answer
    x = 590,855.51

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.