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Finding the Third Proportional to 10,420 and 13,762

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Solution

The third proportional to 10,420 and 13,762 is: 18,175.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,420 : 13,762 = 13,762 : x
  2. Step 2: Convert to fraction form
    10,420/13,762 = 13,762/x
  3. Step 3: Cross multiply
    10,420x = 13,762 × 13,762
  4. Step 4: Simplify right side
    10,420x = 189,392,644
  5. Step 5: Solve for x
    x = 189,392,644/10,420
  6. Step 6: Final answer
    x = 18,175.88

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.