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Finding the Third Proportional to 10,204 and 14,564

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Solution

The third proportional to 10,204 and 14,564 is: 20,786.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,204 : 14,564 = 14,564 : x
  2. Step 2: Convert to fraction form
    10,204/14,564 = 14,564/x
  3. Step 3: Cross multiply
    10,204x = 14,564 × 14,564
  4. Step 4: Simplify right side
    10,204x = 212,110,096
  5. Step 5: Solve for x
    x = 212,110,096/10,204
  6. Step 6: Final answer
    x = 20,786.96

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.