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Finding the Third Proportional to 13,742 and 19,413

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Solution

The third proportional to 13,742 and 19,413 is: 27,424.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,742 : 19,413 = 19,413 : x
  2. Step 2: Convert to fraction form
    13,742/19,413 = 19,413/x
  3. Step 3: Cross multiply
    13,742x = 19,413 × 19,413
  4. Step 4: Simplify right side
    13,742x = 376,864,569
  5. Step 5: Solve for x
    x = 376,864,569/13,742
  6. Step 6: Final answer
    x = 27,424.29

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.