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Finding the Third Proportional to 5,736 and 11,654

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Solution

The third proportional to 5,736 and 11,654 is: 23,677.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,736 : 11,654 = 11,654 : x
  2. Step 2: Convert to fraction form
    5,736/11,654 = 11,654/x
  3. Step 3: Cross multiply
    5,736x = 11,654 × 11,654
  4. Step 4: Simplify right side
    5,736x = 135,815,716
  5. Step 5: Solve for x
    x = 135,815,716/5,736
  6. Step 6: Final answer
    x = 23,677.77

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.