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Finding the Third Proportional to 14,098 and 19,729

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Solution

The third proportional to 14,098 and 19,729 is: 27,609.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,098 : 19,729 = 19,729 : x
  2. Step 2: Convert to fraction form
    14,098/19,729 = 19,729/x
  3. Step 3: Cross multiply
    14,098x = 19,729 × 19,729
  4. Step 4: Simplify right side
    14,098x = 389,233,441
  5. Step 5: Solve for x
    x = 389,233,441/14,098
  6. Step 6: Final answer
    x = 27,609.12

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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.