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Finding the Third Proportional to 6,440 and 13,742

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Solution

The third proportional to 6,440 and 13,742 is: 29,323.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,440 : 13,742 = 13,742 : x
  2. Step 2: Convert to fraction form
    6,440/13,742 = 13,742/x
  3. Step 3: Cross multiply
    6,440x = 13,742 × 13,742
  4. Step 4: Simplify right side
    6,440x = 188,842,564
  5. Step 5: Solve for x
    x = 188,842,564/6,440
  6. Step 6: Final answer
    x = 29,323.38

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.