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Finding the Third Proportional to 10,409 and 15,874

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Solution

The third proportional to 10,409 and 15,874 is: 24,208.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,409 : 15,874 = 15,874 : x
  2. Step 2: Convert to fraction form
    10,409/15,874 = 15,874/x
  3. Step 3: Cross multiply
    10,409x = 15,874 × 15,874
  4. Step 4: Simplify right side
    10,409x = 251,983,876
  5. Step 5: Solve for x
    x = 251,983,876/10,409
  6. Step 6: Final answer
    x = 24,208.27

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.