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Finding the Third Proportional to 5,842 and 7,234

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Solution

The third proportional to 5,842 and 7,234 is: 8,957.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,842 : 7,234 = 7,234 : x
  2. Step 2: Convert to fraction form
    5,842/7,234 = 7,234/x
  3. Step 3: Cross multiply
    5,842x = 7,234 × 7,234
  4. Step 4: Simplify right side
    5,842x = 52,330,756
  5. Step 5: Solve for x
    x = 52,330,756/5,842
  6. Step 6: Final answer
    x = 8,957.68

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Why These Related Problems?

These problems maintain the same ratio (1.24) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.