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Finding the Third Proportional to 13,823 and 21,919

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Solution

The third proportional to 13,823 and 21,919 is: 34,756.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,823 : 21,919 = 21,919 : x
  2. Step 2: Convert to fraction form
    13,823/21,919 = 21,919/x
  3. Step 3: Cross multiply
    13,823x = 21,919 × 21,919
  4. Step 4: Simplify right side
    13,823x = 480,442,561
  5. Step 5: Solve for x
    x = 480,442,561/13,823
  6. Step 6: Final answer
    x = 34,756.75

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.