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Finding the Third Proportional to 12,823 and 19,683

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Solution

The third proportional to 12,823 and 19,683 is: 30,212.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,823 : 19,683 = 19,683 : x
  2. Step 2: Convert to fraction form
    12,823/19,683 = 19,683/x
  3. Step 3: Cross multiply
    12,823x = 19,683 × 19,683
  4. Step 4: Simplify right side
    12,823x = 387,420,489
  5. Step 5: Solve for x
    x = 387,420,489/12,823
  6. Step 6: Final answer
    x = 30,212.94

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.