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Finding the Third Proportional to 414 and 1,003

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Solution

The third proportional to 414 and 1,003 is: 2,429.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 1,003 = 1,003 : x
  2. Step 2: Convert to fraction form
    414/1,003 = 1,003/x
  3. Step 3: Cross multiply
    414x = 1,003 × 1,003
  4. Step 4: Simplify right side
    414x = 1,006,009
  5. Step 5: Solve for x
    x = 1,006,009/414
  6. Step 6: Final answer
    x = 2,429.97

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.