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Finding the Third Proportional to 3,678 and 5,238

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Solution

The third proportional to 3,678 and 5,238 is: 7,459.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,678 : 5,238 = 5,238 : x
  2. Step 2: Convert to fraction form
    3,678/5,238 = 5,238/x
  3. Step 3: Cross multiply
    3,678x = 5,238 × 5,238
  4. Step 4: Simplify right side
    3,678x = 27,436,644
  5. Step 5: Solve for x
    x = 27,436,644/3,678
  6. Step 6: Final answer
    x = 7,459.66

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.