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Finding the Third Proportional to 13,584 and 20,376

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Solution

The third proportional to 13,584 and 20,376 is: 30,564

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,584 : 20,376 = 20,376 : x
  2. Step 2: Convert to fraction form
    13,584/20,376 = 20,376/x
  3. Step 3: Cross multiply
    13,584x = 20,376 × 20,376
  4. Step 4: Simplify right side
    13,584x = 415,181,376
  5. Step 5: Solve for x
    x = 415,181,376/13,584
  6. Step 6: Final answer
    x = 30,564

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.