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Finding the Third Proportional to 6,778 and 7,642

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Solution

The third proportional to 6,778 and 7,642 is: 8,616.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,778 : 7,642 = 7,642 : x
  2. Step 2: Convert to fraction form
    6,778/7,642 = 7,642/x
  3. Step 3: Cross multiply
    6,778x = 7,642 × 7,642
  4. Step 4: Simplify right side
    6,778x = 58,400,164
  5. Step 5: Solve for x
    x = 58,400,164/6,778
  6. Step 6: Final answer
    x = 8,616.14

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.