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Finding the Third Proportional to 14,199 and 19,857

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Solution

The third proportional to 14,199 and 19,857 is: 27,769.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,199 : 19,857 = 19,857 : x
  2. Step 2: Convert to fraction form
    14,199/19,857 = 19,857/x
  3. Step 3: Cross multiply
    14,199x = 19,857 × 19,857
  4. Step 4: Simplify right side
    14,199x = 394,300,449
  5. Step 5: Solve for x
    x = 394,300,449/14,199
  6. Step 6: Final answer
    x = 27,769.59

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.