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Finding the Third Proportional to 5,414 and 7,569

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Solution

The third proportional to 5,414 and 7,569 is: 10,581.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,414 : 7,569 = 7,569 : x
  2. Step 2: Convert to fraction form
    5,414/7,569 = 7,569/x
  3. Step 3: Cross multiply
    5,414x = 7,569 × 7,569
  4. Step 4: Simplify right side
    5,414x = 57,289,761
  5. Step 5: Solve for x
    x = 57,289,761/5,414
  6. Step 6: Final answer
    x = 10,581.78

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.