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Finding the Third Proportional to 257,478 and 538,497

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Solution

The third proportional to 257,478 and 538,497 is: 1,126,228.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,478 : 538,497 = 538,497 : x
  2. Step 2: Convert to fraction form
    257,478/538,497 = 538,497/x
  3. Step 3: Cross multiply
    257,478x = 538,497 × 538,497
  4. Step 4: Simplify right side
    257,478x = 289,979,019,009
  5. Step 5: Solve for x
    x = 289,979,019,009/257,478
  6. Step 6: Final answer
    x = 1,126,228.33

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.