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Finding the Third Proportional to 213,431 and 464,446

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Solution

The third proportional to 213,431 and 464,446 is: 1,010,678.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,431 : 464,446 = 464,446 : x
  2. Step 2: Convert to fraction form
    213,431/464,446 = 464,446/x
  3. Step 3: Cross multiply
    213,431x = 464,446 × 464,446
  4. Step 4: Simplify right side
    213,431x = 215,710,086,916
  5. Step 5: Solve for x
    x = 215,710,086,916/213,431
  6. Step 6: Final answer
    x = 1,010,678.33

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.