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Finding the Third Proportional to 9,729 and 15,408

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Solution

The third proportional to 9,729 and 15,408 is: 24,401.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,729 : 15,408 = 15,408 : x
  2. Step 2: Convert to fraction form
    9,729/15,408 = 15,408/x
  3. Step 3: Cross multiply
    9,729x = 15,408 × 15,408
  4. Step 4: Simplify right side
    9,729x = 237,406,464
  5. Step 5: Solve for x
    x = 237,406,464/9,729
  6. Step 6: Final answer
    x = 24,401.94

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.