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Finding the Third Proportional to 6,821 and 8,077

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Solution

The third proportional to 6,821 and 8,077 is: 9,564.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,821 : 8,077 = 8,077 : x
  2. Step 2: Convert to fraction form
    6,821/8,077 = 8,077/x
  3. Step 3: Cross multiply
    6,821x = 8,077 × 8,077
  4. Step 4: Simplify right side
    6,821x = 65,237,929
  5. Step 5: Solve for x
    x = 65,237,929/6,821
  6. Step 6: Final answer
    x = 9,564.28

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.