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Finding the Third Proportional to 13,564 and 19,374

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Solution

The third proportional to 13,564 and 19,374 is: 27,672.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,564 : 19,374 = 19,374 : x
  2. Step 2: Convert to fraction form
    13,564/19,374 = 19,374/x
  3. Step 3: Cross multiply
    13,564x = 19,374 × 19,374
  4. Step 4: Simplify right side
    13,564x = 375,351,876
  5. Step 5: Solve for x
    x = 375,351,876/13,564
  6. Step 6: Final answer
    x = 27,672.65

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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.