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Finding the Third Proportional to 14,564 and 19,897

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Solution

The third proportional to 14,564 and 19,897 is: 27,182.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,564 : 19,897 = 19,897 : x
  2. Step 2: Convert to fraction form
    14,564/19,897 = 19,897/x
  3. Step 3: Cross multiply
    14,564x = 19,897 × 19,897
  4. Step 4: Simplify right side
    14,564x = 395,890,609
  5. Step 5: Solve for x
    x = 395,890,609/14,564
  6. Step 6: Final answer
    x = 27,182.82

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.