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Finding the Third Proportional to 10,214 and 19,780

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Solution

The third proportional to 10,214 and 19,780 is: 38,305.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,214 : 19,780 = 19,780 : x
  2. Step 2: Convert to fraction form
    10,214/19,780 = 19,780/x
  3. Step 3: Cross multiply
    10,214x = 19,780 × 19,780
  4. Step 4: Simplify right side
    10,214x = 391,248,400
  5. Step 5: Solve for x
    x = 391,248,400/10,214
  6. Step 6: Final answer
    x = 38,305.11

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Why These Related Problems?

These problems maintain the same ratio (1.94) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.