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Finding the Third Proportional to 10,409 and 22,561

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Solution

The third proportional to 10,409 and 22,561 is: 48,899.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,409 : 22,561 = 22,561 : x
  2. Step 2: Convert to fraction form
    10,409/22,561 = 22,561/x
  3. Step 3: Cross multiply
    10,409x = 22,561 × 22,561
  4. Step 4: Simplify right side
    10,409x = 508,998,721
  5. Step 5: Solve for x
    x = 508,998,721/10,409
  6. Step 6: Final answer
    x = 48,899.87

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.