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Finding the Third Proportional to 13,709 and 29,767

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Solution

The third proportional to 13,709 and 29,767 is: 64,634.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,709 : 29,767 = 29,767 : x
  2. Step 2: Convert to fraction form
    13,709/29,767 = 29,767/x
  3. Step 3: Cross multiply
    13,709x = 29,767 × 29,767
  4. Step 4: Simplify right side
    13,709x = 886,074,289
  5. Step 5: Solve for x
    x = 886,074,289/13,709
  6. Step 6: Final answer
    x = 64,634.49

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.