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Finding the Third Proportional to 7,699 and 9,837

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Solution

The third proportional to 7,699 and 9,837 is: 12,568.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,699 : 9,837 = 9,837 : x
  2. Step 2: Convert to fraction form
    7,699/9,837 = 9,837/x
  3. Step 3: Cross multiply
    7,699x = 9,837 × 9,837
  4. Step 4: Simplify right side
    7,699x = 96,766,569
  5. Step 5: Solve for x
    x = 96,766,569/7,699
  6. Step 6: Final answer
    x = 12,568.72

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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.