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Finding the Third Proportional to 10,419 and 23,241

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Solution

The third proportional to 10,419 and 23,241 is: 51,842.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,419 : 23,241 = 23,241 : x
  2. Step 2: Convert to fraction form
    10,419/23,241 = 23,241/x
  3. Step 3: Cross multiply
    10,419x = 23,241 × 23,241
  4. Step 4: Simplify right side
    10,419x = 540,144,081
  5. Step 5: Solve for x
    x = 540,144,081/10,419
  6. Step 6: Final answer
    x = 51,842.22

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.