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Finding the Third Proportional to 414 and 872

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Solution

The third proportional to 414 and 872 is: 1,836.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 872 = 872 : x
  2. Step 2: Convert to fraction form
    414/872 = 872/x
  3. Step 3: Cross multiply
    414x = 872 × 872
  4. Step 4: Simplify right side
    414x = 760,384
  5. Step 5: Solve for x
    x = 760,384/414
  6. Step 6: Final answer
    x = 1,836.68

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.