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Finding the Third Proportional to 5,842 and 6,706

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Solution

The third proportional to 5,842 and 6,706 is: 7,697.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,842 : 6,706 = 6,706 : x
  2. Step 2: Convert to fraction form
    5,842/6,706 = 6,706/x
  3. Step 3: Cross multiply
    5,842x = 6,706 × 6,706
  4. Step 4: Simplify right side
    5,842x = 44,970,436
  5. Step 5: Solve for x
    x = 44,970,436/5,842
  6. Step 6: Final answer
    x = 7,697.78

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.