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Finding the Third Proportional to 10,299 and 15,413

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Solution

The third proportional to 10,299 and 15,413 is: 23,066.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,299 : 15,413 = 15,413 : x
  2. Step 2: Convert to fraction form
    10,299/15,413 = 15,413/x
  3. Step 3: Cross multiply
    10,299x = 15,413 × 15,413
  4. Step 4: Simplify right side
    10,299x = 237,560,569
  5. Step 5: Solve for x
    x = 237,560,569/10,299
  6. Step 6: Final answer
    x = 23,066.37

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.