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Finding the Third Proportional to 9,731 and 14,209

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Solution

The third proportional to 9,731 and 14,209 is: 20,747.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,731 : 14,209 = 14,209 : x
  2. Step 2: Convert to fraction form
    9,731/14,209 = 14,209/x
  3. Step 3: Cross multiply
    9,731x = 14,209 × 14,209
  4. Step 4: Simplify right side
    9,731x = 201,895,681
  5. Step 5: Solve for x
    x = 201,895,681/9,731
  6. Step 6: Final answer
    x = 20,747.68

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.