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Finding the Third Proportional to 9,730 and 11,234

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Solution

The third proportional to 9,730 and 11,234 is: 12,970.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,730 : 11,234 = 11,234 : x
  2. Step 2: Convert to fraction form
    9,730/11,234 = 11,234/x
  3. Step 3: Cross multiply
    9,730x = 11,234 × 11,234
  4. Step 4: Simplify right side
    9,730x = 126,202,756
  5. Step 5: Solve for x
    x = 126,202,756/9,730
  6. Step 6: Final answer
    x = 12,970.48

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.