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Finding the Third Proportional to 9,730 and 20,296

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Solution

The third proportional to 9,730 and 20,296 is: 42,335.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,730 : 20,296 = 20,296 : x
  2. Step 2: Convert to fraction form
    9,730/20,296 = 20,296/x
  3. Step 3: Cross multiply
    9,730x = 20,296 × 20,296
  4. Step 4: Simplify right side
    9,730x = 411,927,616
  5. Step 5: Solve for x
    x = 411,927,616/9,730
  6. Step 6: Final answer
    x = 42,335.83

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.