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Finding the Third Proportional to 13,691 and 19,564

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Solution

The third proportional to 13,691 and 19,564 is: 27,956.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,691 : 19,564 = 19,564 : x
  2. Step 2: Convert to fraction form
    13,691/19,564 = 19,564/x
  3. Step 3: Cross multiply
    13,691x = 19,564 × 19,564
  4. Step 4: Simplify right side
    13,691x = 382,750,096
  5. Step 5: Solve for x
    x = 382,750,096/13,691
  6. Step 6: Final answer
    x = 27,956.33

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.