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Finding the Third Proportional to 5,398 and 11,564

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Solution

The third proportional to 5,398 and 11,564 is: 24,773.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,398 : 11,564 = 11,564 : x
  2. Step 2: Convert to fraction form
    5,398/11,564 = 11,564/x
  3. Step 3: Cross multiply
    5,398x = 11,564 × 11,564
  4. Step 4: Simplify right side
    5,398x = 133,726,096
  5. Step 5: Solve for x
    x = 133,726,096/5,398
  6. Step 6: Final answer
    x = 24,773.27

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.