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Finding the Third Proportional to 132,049 and 280,459

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Solution

The third proportional to 132,049 and 280,459 is: 595,667.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    132,049 : 280,459 = 280,459 : x
  2. Step 2: Convert to fraction form
    132,049/280,459 = 280,459/x
  3. Step 3: Cross multiply
    132,049x = 280,459 × 280,459
  4. Step 4: Simplify right side
    132,049x = 78,657,250,681
  5. Step 5: Solve for x
    x = 78,657,250,681/132,049
  6. Step 6: Final answer
    x = 595,667.14

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.