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Finding the Third Proportional to 9,586 and 14,106

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Solution

The third proportional to 9,586 and 14,106 is: 20,757.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,586 : 14,106 = 14,106 : x
  2. Step 2: Convert to fraction form
    9,586/14,106 = 14,106/x
  3. Step 3: Cross multiply
    9,586x = 14,106 × 14,106
  4. Step 4: Simplify right side
    9,586x = 198,979,236
  5. Step 5: Solve for x
    x = 198,979,236/9,586
  6. Step 6: Final answer
    x = 20,757.27

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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.