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Finding the Third Proportional to 10,586 and 23,869

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Solution

The third proportional to 10,586 and 23,869 is: 53,819.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,586 : 23,869 = 23,869 : x
  2. Step 2: Convert to fraction form
    10,586/23,869 = 23,869/x
  3. Step 3: Cross multiply
    10,586x = 23,869 × 23,869
  4. Step 4: Simplify right side
    10,586x = 569,729,161
  5. Step 5: Solve for x
    x = 569,729,161/10,586
  6. Step 6: Final answer
    x = 53,819.12

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Why These Related Problems?

These problems maintain the same ratio (2.25) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.