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Finding the Third Proportional to 257,461 and 538,462

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Solution

The third proportional to 257,461 and 538,462 is: 1,126,156.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,461 : 538,462 = 538,462 : x
  2. Step 2: Convert to fraction form
    257,461/538,462 = 538,462/x
  3. Step 3: Cross multiply
    257,461x = 538,462 × 538,462
  4. Step 4: Simplify right side
    257,461x = 289,941,325,444
  5. Step 5: Solve for x
    x = 289,941,325,444/257,461
  6. Step 6: Final answer
    x = 1,126,156.29

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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.