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Finding the Third Proportional to 4,214 and 9,797

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Solution

The third proportional to 4,214 and 9,797 is: 22,776.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,214 : 9,797 = 9,797 : x
  2. Step 2: Convert to fraction form
    4,214/9,797 = 9,797/x
  3. Step 3: Cross multiply
    4,214x = 9,797 × 9,797
  4. Step 4: Simplify right side
    4,214x = 95,981,209
  5. Step 5: Solve for x
    x = 95,981,209/4,214
  6. Step 6: Final answer
    x = 22,776.75

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.