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Finding the Third Proportional to 6,821 and 9,786

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Solution

The third proportional to 6,821 and 9,786 is: 14,039.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,821 : 9,786 = 9,786 : x
  2. Step 2: Convert to fraction form
    6,821/9,786 = 9,786/x
  3. Step 3: Cross multiply
    6,821x = 9,786 × 9,786
  4. Step 4: Simplify right side
    6,821x = 95,765,796
  5. Step 5: Solve for x
    x = 95,765,796/6,821
  6. Step 6: Final answer
    x = 14,039.85

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.