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Finding the Third Proportional to 13,782 and 20,217

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Solution

The third proportional to 13,782 and 20,217 is: 29,656.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,782 : 20,217 = 20,217 : x
  2. Step 2: Convert to fraction form
    13,782/20,217 = 20,217/x
  3. Step 3: Cross multiply
    13,782x = 20,217 × 20,217
  4. Step 4: Simplify right side
    13,782x = 408,727,089
  5. Step 5: Solve for x
    x = 408,727,089/13,782
  6. Step 6: Final answer
    x = 29,656.59

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.