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Finding the Third Proportional to 414 and 459

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Solution

The third proportional to 414 and 459 is: 508.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 459 = 459 : x
  2. Step 2: Convert to fraction form
    414/459 = 459/x
  3. Step 3: Cross multiply
    414x = 459 × 459
  4. Step 4: Simplify right side
    414x = 210,681
  5. Step 5: Solve for x
    x = 210,681/414
  6. Step 6: Final answer
    x = 508.89

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.