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Finding the Third Proportional to 3,709 and 7,834

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Solution

The third proportional to 3,709 and 7,834 is: 16,546.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,709 : 7,834 = 7,834 : x
  2. Step 2: Convert to fraction form
    3,709/7,834 = 7,834/x
  3. Step 3: Cross multiply
    3,709x = 7,834 × 7,834
  4. Step 4: Simplify right side
    3,709x = 61,371,556
  5. Step 5: Solve for x
    x = 61,371,556/3,709
  6. Step 6: Final answer
    x = 16,546.66

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.