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Finding the Third Proportional to 6,864 and 9,678

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Solution

The third proportional to 6,864 and 9,678 is: 13,645.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,864 : 9,678 = 9,678 : x
  2. Step 2: Convert to fraction form
    6,864/9,678 = 9,678/x
  3. Step 3: Cross multiply
    6,864x = 9,678 × 9,678
  4. Step 4: Simplify right side
    6,864x = 93,663,684
  5. Step 5: Solve for x
    x = 93,663,684/6,864
  6. Step 6: Final answer
    x = 13,645.64

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.