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Finding the Third Proportional to 5,978 and 6,770

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Solution

The third proportional to 5,978 and 6,770 is: 7,666.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,978 : 6,770 = 6,770 : x
  2. Step 2: Convert to fraction form
    5,978/6,770 = 6,770/x
  3. Step 3: Cross multiply
    5,978x = 6,770 × 6,770
  4. Step 4: Simplify right side
    5,978x = 45,832,900
  5. Step 5: Solve for x
    x = 45,832,900/5,978
  6. Step 6: Final answer
    x = 7,666.93

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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.