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Finding the Third Proportional to 9,665 and 14,214

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Solution

The third proportional to 9,665 and 14,214 is: 20,904.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,665 : 14,214 = 14,214 : x
  2. Step 2: Convert to fraction form
    9,665/14,214 = 14,214/x
  3. Step 3: Cross multiply
    9,665x = 14,214 × 14,214
  4. Step 4: Simplify right side
    9,665x = 202,037,796
  5. Step 5: Solve for x
    x = 202,037,796/9,665
  6. Step 6: Final answer
    x = 20,904.07

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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.