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Finding the Third Proportional to 10,289 and 14,569

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Solution

The third proportional to 10,289 and 14,569 is: 20,629.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,289 : 14,569 = 14,569 : x
  2. Step 2: Convert to fraction form
    10,289/14,569 = 14,569/x
  3. Step 3: Cross multiply
    10,289x = 14,569 × 14,569
  4. Step 4: Simplify right side
    10,289x = 212,255,761
  5. Step 5: Solve for x
    x = 212,255,761/10,289
  6. Step 6: Final answer
    x = 20,629.39

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.