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Finding the Third Proportional to 5,684 and 7,678

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Solution

The third proportional to 5,684 and 7,678 is: 10,371.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,684 : 7,678 = 7,678 : x
  2. Step 2: Convert to fraction form
    5,684/7,678 = 7,678/x
  3. Step 3: Cross multiply
    5,684x = 7,678 × 7,678
  4. Step 4: Simplify right side
    5,684x = 58,951,684
  5. Step 5: Solve for x
    x = 58,951,684/5,684
  6. Step 6: Final answer
    x = 10,371.51

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.