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Finding the Third Proportional to 7,678 and 9,833

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Solution

The third proportional to 7,678 and 9,833 is: 12,592.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,678 : 9,833 = 9,833 : x
  2. Step 2: Convert to fraction form
    7,678/9,833 = 9,833/x
  3. Step 3: Cross multiply
    7,678x = 9,833 × 9,833
  4. Step 4: Simplify right side
    7,678x = 96,687,889
  5. Step 5: Solve for x
    x = 96,687,889/7,678
  6. Step 6: Final answer
    x = 12,592.85

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.