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Finding the Third Proportional to 10,591 and 16,411

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Solution

The third proportional to 10,591 and 16,411 is: 25,429.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,591 : 16,411 = 16,411 : x
  2. Step 2: Convert to fraction form
    10,591/16,411 = 16,411/x
  3. Step 3: Cross multiply
    10,591x = 16,411 × 16,411
  4. Step 4: Simplify right side
    10,591x = 269,320,921
  5. Step 5: Solve for x
    x = 269,320,921/10,591
  6. Step 6: Final answer
    x = 25,429.22

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.